IIT JAM 2026 Syllabus for Physics, Chemistry & Mathematics

    Name of the               Chapter

            Name of the Topics

        General                   Biology

Taxonomy, Heredity, Genetic variation, Conservation, Principles of ecology, Evolution, Techniques in modern biology.

        Biochemistry and Physiology

Carbohydrates, Proteins, Lipids, Nucleic acids, Enzymes, Vitamins, Hormones, Metabolism (Glycolysis, TCA cycle, Oxidative Phosphorylation, Photosynthesis), Nitrogen Fixation, Fertilization and Osmoregulation, Vertebrates-Nervous system, Endocrine system, Vascular system, Immune system, Digestive system and Reproductive System.

Basic Biotechnology

Tissue culture, Application of enzymes, Antigen-antibody interaction, Antibody production, Diagnostic aids.

Molecular Biology

DNA, RNA, Replication, Transcription, Translation, Proteins, Lipids and Membranes, Operon model, Gene transfer.

Cell Biology

Cell cycle, Cytoskeletal elements, Mitochondria, Endoplasmic reticulum, Chloroplast, Golgi apparatus, Signalling.

Microbiology

Isolation, Cultivation, Structural features of virus, Bacteria, Fungi, Protozoa, Pathogenic microorganisms.

            Name of the Book

Author of the book

Essentials: Biology Standard

Randy Mcgonegal & Alan Damon

Physiology and Biochemistry in Modern Medicine

John James Rickard MacLeod

Molecular Biology of the Gene

James D.Watson

Name of the Chapter

Name of the Topics

Atomic Structure

Bohr’s theory and Schrodinger wave equation, Periodicity in properties, Chemical bonding, Properties of s, p, d and f block elements, Complex formation, Coordination compounds, Chemical equilibrium, Chemical thermodynamics (first and second law); Chemical kinetics (zero, first, second and third-order reactions), Photochemistry, Electrochemistry, Acid-base concepts, Stereochemistry of carbon compounds, Inductive, electrometric, conjugative effects and resonance.

Chemistry of Functional Groups

Hydrocarbons, alkyl halides, alcohols, aldehydes, ketones, carboxylic acids, amines and their derivatives, Aromatic hydrocarbons, halides, nitro and amino compounds, phenols, diazonium salts, carboxylic and sulphonic acids, Mechanism of organic reactions.

Synthetic polymers

Biomolecules, amino acids, proteins, nucleic acids, lipids and carbohydrates (polysaccharides), Instrumental techniques – chromatography (TLC, HPLC), electrophoresis, UV-Vis, IR and NMR spectroscopy, mass spectrometry

Sets, Relations and Functions

Mathematical Induction

Logarithms

Complex numbers

Linear and Quadratic equations

Sequences and Series

Trigonometry

Cartesian System of Rectangular Coordinates

Straight lines and Family

Circles

Conic Sections

Permutations and Combinations

Binomial Theorem

Exponential and Logarithmic Series

Mathematical Logic

Statistics

Three Dimensional Geometry

Vectors

Matrices and Determinants

Boolean Algebra

Probability

Functions

limits and Continuity

Differentiation

Application of Derivatives

Definite and Indefinite Integrals

Differential Equations

Physical World and Measurement

Elementary Statics and Dynamics

Kinematics

Laws of Motion

Work

Energy and Power

Electrostatics

Current electricity

Magnetic Effects of Current and Magnetism

Electromagnetic Induction and Alternating Current

Electromagnetic waves

Optics

Dual Nature of Matter and Radiations

Atomic Nucleus

Solids and Semiconductor Devices

Principles of Communication

Motion of System of Particles and Rigid Body

Gravitation

Mechanics of Solids and Fluids

Heat and Thermodynamics

Oscillations, Waves

Name of the Chapter

Topics

Basic Mathematical Concepts

Functions, maxima and minima, integrals, ordinary differential equations, vectors and matrices, determinants, elementary statistics, and probability theory.

Atomic and Molecular Structure

Fundamental particles, Bohr’s theory of the hydrogen-like atom, wave-particle duality, uncertainty principle, Schrödinger’s wave equation, quantum numbers, shapes of orbitals, Hund’s rule and Pauli’s exclusion principle, electronic configuration of simple homonuclear diatomic molecules.

Theory of Gases

Equation of state for ideal and non-ideal (van der Waals) gases, Kinetic theory of gases, Maxwell-Boltzmann distribution law, equipartition of energy.

Solid-state

Crystals and crystal systems, X-rays, NaCl and KCl structures, close packing, atomic and ionic radii, radius ratio rules, lattice energy, Born-Haber cycle, isomorphism, the heat capacity of solids.

Chemical Thermodynamics

Reversible and irreversible processes, first law and its application to ideal and no ideal gases, thermochemistry, second law, entropy, and free energy, Criteria for spontaneity.

Chemical and Phase Equilibria

Law of mass action, Kp, Kc, Kx and Kn, the effect of temperature on K, ionic equilibria in solutions, pH and buffer solutions, hydrolysis, solubility product, phase equilibria–phase rule and its application to one-component and two-component systems, colligative properties.

Electrochemistry

Conductance and its applications, transport number, galvanic cells, EMF and free energy, concentration cells with and without transport, polarography, concentration cells with and without transport, Debye-Huckel-Onsager theory of strong electrolytes.

Chemical Kinetics

Reactions of various orders, Arrhenius equation, collision theory, transition state theory, chain reactions – normal and branched, enzyme kinetics, photochemical processes, catalysis.

Adsorption

Gibbs adsorption equation, adsorption isotherm, types of adsorption, the surface area of adsorbents, surface films on liquids.

Spectroscopy

Beer-Lambert law, fundamental concepts of rotational, vibrational, electronic and magnetic resonance spectroscopy

Name of the Chapter

Topics

Basic Concepts in Organic Chemistry and Stereochemistry

Electronic effects (resonance, inductive, hyperconjugation) and steric effects and its applications (acid/base property), optical isomerism in compounds with and without any stereo Centres (allenes, biphenyls), conformation of acyclic systems (substituted ethane/n-propane/n-butane) and cyclic systems (mono- and di-substituted cyclohexanes).

Organic Reaction Mechanism and Synthetic Applications

Chemistry of reactive intermediates (carbocations, carbanions, free radicals, carbenes, nitrenes, benzynes etc…), Hofmann-Curtius-Lossen rearrangement, Wolff rearrangement, Simmons-Smith reaction, Reimer-Tiemann reaction, Michael reaction, Darzens reaction, Wittig reaction and McMurry reaction, Pinacol-pinacolone, Favorskii, benzilic acid rearrangement, dienone-phenol rearrangement, Baeyer-Villeger reaction; oxidation and reduction reactions in organic chemistry, organometallic reagents in organic synthesis (Grignard, organolithium and organocopper), Diels-Alder, electrocyclic and sigmatropic reactions, functional group inter-conversions and structural problems using chemical reactions.

Qualitative Organic Analysis

Identification of functional groups by chemical tests; elementary UV, IR and 1H NMR spectroscopic techniques as tools for structural elucidation.

Natural Products Chemistry

Chemistry of alkaloids, steroids, terpenes, carbohydrates, amino acids, peptides, and nucleic acids.

Aromatic and Heterocyclic Chemistry

Monocyclic, bicyclic and tricyclic aromatic hydrocarbons, and monocyclic compounds with one hetero atom: synthesis, reactivity, and properties.

Name of the chapter

Topics

Periodic Table

Periodic classification of elements and periodicity in properties, general methods of isolation and purification of elements

Chemical Bonding and Shapes of Compounds

Types of bonding, VSEPR theory, and shapes of molecules, hybridization, dipole moment, ionic solids, the structure of NaCl, CsCl, diamond and graphite, lattice energy

Main Group Elements (s and p blocks)

General concepts on group relationships and gradation in properties, the structure of electron-deficient compounds involving main group elements

Transition Metals (d block)

Characteristics of 3d elements, oxide, hydroxide, and salts of first row metals

Coordination complexes

structure, isomerism, reaction mechanism, and electronic spectra, VB, MO and Crystal Field theoretical approaches for structure, color and magnetic properties of metal complexes, organometallic compounds having legends with back bonding capabilities such as metal carbonyls, carbenes, nitrosyls and metallocenes, homogenous catalysis

Bioinorganic Chemistry

Essentials and trace elements of life, basic reactions in the biological systems and the role of metal ions, especially Fe2+, Fe3+, Cu2+ and Zn2+, structure and function of Haemoglobin and myoglobin and carbonic anhydrase

Instrumental Methods of Analysis

Basic principles, instrumentations and simple applications of conductometry, potentiometry and UV-vis spectrophotometry; analysis of water, air and soil samples

Analytical Chemistry

Principles of qualitative and quantitative analysis, acid-base, oxidation-reduction and complexometric titrations using EDTA, precipitation reactions, use of indicators, use of organic reagents in inorganic analysis, radioactivity, nuclear reactions, applications of isotopes

          Name of the Book

        Author of the Book 

Chemistry Higher Level

Catrin Brown and Mike Ford

Inorganic Chemistry

R.L. Dutta and GS De.

Organic Chemistry

Jonathan Clyden and Nick Greeves

Name of the Chapter

Topics

The Planet Earth

Origin of the Solar System and the Earth, Geosphere and the composition of the Earth, Shape and size of the earth, Earth-moon system, Formation of continents and oceans, Dating rocks and age of the Earth, Volcanism and volcanic landforms, Interior of earth, Earthquakes, Earth’s magnetism and gravity, Isostasy, Elements of Plate tectonics, Orogenic cycles

Geomorphology

Weathering and erosion, Transportation and deposition due to wind, ice, river, sea, and resulting landforms, Structurally controlled landforms

Structural Geology

Concept of stratum, Contour, Outcrop patterns, Maps and cross-sections, Dip and strike, Classification and origin of folds, faults, joints, unconformities, foliations and lineations, shear zones

Stereographic

Stereographic and equal-area projections of planes and lines, computation of true thickness of beds from outcrops and bore-holes

Paleontology

Major steps in the evolution of life forms, Fossils and their mode of preservation and utility, Morphological characters, major evolutionary trends and ages of important groups of animals – Brachiopoda, Mollusca, Trilobita, Graptoloidea, Anthozoa, Echinodermata, Gondwana plant fossils, Elementary idea of vertebrate fossils in India

Stratigraphy

Principles of stratigraphy, Litho-, Chrono- and biostratigraphic classification, distribution and classification of the stratigraphic horizons of India from Archaean to Recent

Mineralogy

Symmetry and forms in common crystal classes, Physical properties of minerals, Isomorphism and polymorphism, Classification of minerals, Structure of silicates, Mineralogy of common rock-forming minerals, Mode of occurrence of minerals in rocks

Transmitted

Transmitted polarized light microscopy and optical properties of uniaxial and biaxial minerals

Petrology

Definition and classification of rocks, Igneous rocks-forms of igneous bodies, Crystallization from magma, classification, association and genesis of igneous rocks, Sedimentary rocks – classification, texture and structure; size and shape of sedimentary bodies ,Metamorphic rocks – classification, facies, zones and texture

Characteristic

Characteristic mineral assemblages of pelites in the Barrovian zones and mafic rocks in common facies

Economic Geology

Properties of common economic minerals, General processes of formation of mineral deposits, Physical characters, Mode of occurrence and distribution in India both of metallic and non-metallic mineral deposits, Coal and petroleum occurrences in India

Applied Geology

Ground Water, Principles of Engineering Geology

Name of the Book

Author of the Book

IIT JAM: MSc Geology Previous Years Paper

Ajhar Hussain

GATE Geology & Geophysics

Amaresh Singh & Jitendra Mishra

An Introduction to Geology

VS Joji

Name of the Chapter

Topics

Sequences and Series of Real Numbers

Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem

Series of real numbers, absolute convergence, tests of convergence for series of positive terms

comparison test, ratio test, root test, Leibniz test for convergence of alternating series. Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, maxima and minima

Functions of Two or Three Real Variables

Limit, continuity, partial derivatives, differentiability, maxima and minima

Integral Calculus

Integration as the inverse process of differentiation, definite integrals and their properties, fundamental theorem of calculus

Double and triple integrals

Change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals

Differential Equations

Ordinary differential equations of the first order of the form y’=f(x,y), Bernoulli’s equation, exact differential equations, integrating factor, orthogonal trajectories, homogeneous differential equations, variable separable equations, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation

Vector Calculus

Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes and Gauss theorems

Group Theory

Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange’s Theorem for finite groups, group homomorphisms and basic concepts of quotient groups

Linear Algebra

Finite-dimensional vector spaces, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem

Rank and inverse of a matrix

Determinant, solutions of systems of linear equations, consistency conditions, eigenvalues and eigenvectors for matrices, Cayley-Hamilton theorem

Real Analysis

Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylor’s series, radius and interval of convergence, term-wise differentiation and integration of power series

Name of the Chapter

Topics

Sequences and Series

Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers

Differential Calculus

Limits, continuity and differentiability of functions of one and two variables. Rolle’s theorem, mean value theorems, Taylor’s theorem, indeterminate forms, maxima and minima of functions of one and two variables

Integral Calculus

Fundamental theorems of integral calculus

Double and triple integrals

applications of definite integrals, arc lengths, areas, and volumes

Matrices

Rank, the inverse of a matrix, Systems of linear equations, Linear transformations, eigenvalues, and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices

Name of the Chapter

Topics

Probability

Axiomatic definition of probability and properties, conditional probability, multiplication rule, Theorem of total probability, Bayes’ theorem and independence of events

Random Variables

Probability mass function, probability density function, and cumulative distribution functions, distribution of a function of a random variable, Mathematical expectation, moments and moment generating function, Chebyshev’s inequality

Standard Distributions

Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution

Joint Distributions

Joint, marginal and conditional distributions, Distribution of functions of random variables, Joint moment generating function, Product moments, correlation, simple linear regression, Independence of random variables

Sampling distributions

Chi-square, t and F distributions, and their properties

Limit Theorems

Weak law of large numbers, Central limit theorem (i.i.d.with finite variance case only)

Estimation

Unbiasedness, consistency and efficiency of estimators, method of moments and method of maximum likelihood, Sufficiency, factorization theorem, Rao-Blackwell and Lehmann-Scheffe theorems, uniformly minimum variance unbiased estimators, Rao-Cramer inequality, Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions

Testing of Hypotheses

Basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses, Likelihood ratio tests for parameters of univariate normal distribution

      Name of the Book 

Author of the Book

Solutions To IIT JAM For Mathematical Statistics (Paperback, Mohd. Arshad, Amit kumar Miishra)

Mohd. Arshad, Amit kumar Miishra

Mathematical Statistics For Iit Jam Complete Study Material With Topic Wise Advance Analysis + Model Solved Papers (SPIRAL, SOURAV SIR’S CLASSES)

SOURAV SIR’S CLASSES

Study Material for IIT JAM Mathematics

Sourav Sir’s Classes

Name  of the Chapter

Topics

Mathematical Methods

Calculus of single and multiple variables, partial derivatives, Jacobian, imperfect and perfect differentials, Taylor expansion, Fourier series, Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green’s theorem, Stokes’ theorem, First order equations and linear second-order differential equations with constant coefficients, Matrices and determinants, Algebra of complex numbers.

Mechanics and General Properties of Matter

Newton’s laws of motion and applications, Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems, uniformly rotating frame, centrifugal and Coriolis forces, Motion under a central force, Kepler’s laws, Gravitational Law and field, Conservative and nonconservative forces, System of particles, Centre of mass, equation of motion of the CM, conservation of linear and angular momentum, conservation of energy, variable mass systems, Elastic and inelastic collisions. Rigid body motion, fixed axis rotations, rotation and translation, moments of Inertia and products of Inertia, parallel and perpendicular axes theorem, Principal moments and axes, Kinematics of moving fluids, equation of continuity, Euler’s equation, Bernoulli’s theorem, Oscillations, Waves and Optics: Differential equation for simple harmonic oscillator and its general solution, Superposition of two or more simple harmonic oscillators, Lissajous figures, Damped and forced oscillators, resonance, Wave equation, traveling and standing waves in one-dimension. Energy density and energy transmission in waves, Group velocity and phase velocity, Sound waves in media, Doppler Effect, Fermat’s Principle, General theory of image formation,Thick lens, thin lens and lens combinations, Interference of light, optical path retardation, Fraunhofer diffraction,Rayleigh criterion and resolving power, Diffraction gratings, Polarization: linear, circular and elliptic polarization, Double refraction and optical rotation

Electricity and Magnetism

Coulomb’s law, Gauss’s law, Electric field and potential, Electrostatic boundary conditions, Solution of Laplace’s equation for simple cases. Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy, Biot-Savart law, Ampere’s law, Faraday’s law of electromagnetic induction, Self and mutual inductance, Alternating currents, Simple DC and AC circuits with R, L and C components, Displacement current, Maxwell’s equations and plane electromagnetic waves, Poynting’s theorem, reflection and refraction at a dielectric interface, transmission and reflection coefficients (normal incidence only), Lorentz Force and motion of charged particles in electric and magnetic fields,Kinetic theory

Thermodynamics

Elements of Kinetic theory of gases, Velocity distribution and Equipartition of energy, Specific heat of Mono-, di- and triatomic gases, Ideal gas, van-der-Waals gas and equation of state,Mean free path, Laws of 25 thermodynamics, Zeroth law and concept of thermal equilibrium, First law and its consequences,Isothermal and adiabatic processes, Reversible, irreversible and quasi static processes, Second law and entropy, Carnot cycle, Maxwell’s thermodynamic relations and simple applications, Thermodynamic potentials and their applications, Phase transitions and Clausius-Clapeyron equation, Ideas of ensembles, MaxwellBoltzmann, Fermi-Dirac and Bose-Einstein distributions

Modern Physics

Inertial frames and Galilean invariance, Postulates of special relativity. Lorentz transformations, Length contraction, time dilation, Relativistic velocity addition theorem, mass energy equivalence, Blackbody radiation, photoelectric effect, Compton effect, Bohr’s atomic model, X-rays, Wave-particle duality, Uncertainty principle, the superposition principle, calculation of expectation values, Schrödinger equation and its solution for one, two and three dimensional boxes, Solution of Schrödinger equation for the one dimensional harmonic oscillator. Reflection and transmission at a step potential, Pauli exclusion principle, Structure of atomic nucleus, mass and binding energy, Radioactivity and its applications, Laws of radioactive decay, Solid State Physics, Devices and Electronics: Crystal structure, Bravais lattices and basis, Miller indices, X-ray diffraction and Bragg’s law, Intrinsic and extrinsic semiconductors, variation of resistivity with temperature, Fermi level, p-n junction diode, I-V characteristics, Zener diode and its applications, BJT- characteristics in CB, CE, CC modes, Single stage amplifier, two stage R-C coupled amplifiers

Simple Oscillators

Barkhausen condition, sinusoidal oscillators, OP AMP and applications, Inverting and non-inverting amplifier, Boolean algebra, Binary number systems, conversion from one system to another system, binary addition and subtraction, Logic Gates AND, OR, NOT, NAND, NOR exclusive OR Truth tables, combination of gates, de Morgan’s theorem

Name of the Book

Author of the Book

IIT JAM Physics Solved Papers & Practice Set

Atique Hasan

IIT JAM Theory & Practice Book

Sushil K Tomar

IIT JAM Theory & Practice A Comprehensive Book

Sushil K Tomar

Name of the Chapter

Topics

Consumer theory

Preference, utility and representation theorem, budget constraint, choice, demand (ordinary and compensated), Slutsky equations, choice under risk and uncertainty, revealed preference axioms

Production, costs with perfectly competitive markets

Technology, isoquants, production with one and more variable inputs, returns to scale, short run and long run costs, cost curves in the short run and long run, perfect competition in markets

General equilibrium and welfare

Equilibrium and efficiency under pure exchange and production, welfare economics, theorems of welfare economics

Market structure

Monopoly, pricing with market power, price discrimination (first, second and third), monopolistic competition and oligopoly

Game theory

Strategic form games, Nash equilibrium, mixed extension and mixed strategy Nash equilibrium, iterated elimination of dominated strategies, examples: Cournot, Bertrand duopolies, Prisoner’s dilemma, cooperative game theory: Shapley value, Nash bargaining

Public goods and market failure

Externalities, public goods and markets with asymmetric information (adverse selection and moral hazard), VCG mechanism and transfer rules

Name of the Chapter

Topics

National Income Accounting

Structure, key concepts, measurements, and circular flow of income – for a closed and open economy, money, fiscal and foreign sector variables – concepts and measurements

Behavioral and Technological Functions 

Consumption functions – absolute income hypothesis, life-cycle, and permanent income hypothesis, investment functions- Keynesian, money demand and supply functions, production function

Business Cycles and Economic Models

Business cycles-facts and features, the Classical model of the business cycle. the Keynesian model of the business cycle, simple Keynesian cross model of income and employment determination and the multiplier (in a closed economy), IS-LM Model, Hicks’ IS-LM synthesis, role of monetary and fiscal policy

Business Cycles and Economic Models (Open Economy)

Open economy, Mundell-Fleming model, Keynesian flexible price (aggregate demand and aggregate supply) model, role of monetary and fiscal policy

Inflation and Unemployment

Inflation – theories, measurement, causes, and effects, Unemployment -types, measurement, causes, and effects

Growth Models

Harrod-Domar, Solow and Neoclassical growth models

Topics

Probability theory, Sample spaces and events, Axioms of probability and their properties, conditional probability and Bayes’ rule, independent events

Random variables and probability distributions, probability distributions, expected values and functions of random variables, properties of commonly used discrete and continuous distributions

Random sampling, Density and distribution functions for jointly distributed random variables, computing expected values of jointly distributed random variables, covariance and correlation coefficients

Point and interval estimation, estimation of population parameters using methods of moments and maximum likelihood procedures, properties of estimators, confidence intervals

Hypothesis testing, distributions of test statistics, testing hypotheses related to population parame- 32 ters, Type I and Type II errors, the power of a test, tests for comparing parameters from two samples

Name of the Chapter

Topics

Indian economy before 1950

Transfer of tribute, deindustrialization of India

Planning and Indian development

Planning models, relation between agricultural and industrial growth, challenges faced by Indian planning

Indian economy after 1991

Balance of payments crisis in 1991, major aspects of economic reforms in India after 1991, reforms in trade and foreign investment

Banking, finance and macroeconomic policies

Aspects of banking in India, CRR and SLR, financial sector reforms in India, fiscal deficit, savings and investment rates in India

Inequalities in social development

India’s achievements in health, education and other social sectors, disparities between Indian States in human development

Poverty

Methodology of poverty estimation, Issues in poverty estimation in India

India’s labour market

Unemployment, labour force participation rates

Name of the Chapter

Topics

Preliminaries and Functions of one real variable

a. Set theory and number theory, Graphs, elementary types of functions: quadratic, polynomial, power, exponential, logarithmic, sequences and series: convergence, algebraic properties and applications

b. Continuous functions: characteristics, properties with respect to various operations and applications

c. Differentiable functions: characteristics, properties with respect to various operations and applications

d. Second and higher order derivatives: properties and applications

Single-variable optimization

Geometric properties of functions: convex functions, their characterisations and applications, local and global optima: geometric and calculus-based characterisations, and applications.

Linear algebra

Vector spaces – algebraic and geometric properties, scalar products, norms, orthogonality, linear transformations: properties, matrix representations and elementary operations, systems of linear equations: properties of their solution sets, determinants: characterisation, properties and applications

Functions of several real variables

Geometric representations – graphs and level curves, differentiable functions: characteristics, properties with respect to various operations and applications, second order derivatives: properties and applications, the implicit function theorem, and application to comparative statics problems, homogeneous and homothetic functions: characteristics and applications

Multivariate optimization

Convex sets, geometric properties of functions: convex functions, their characteristics, properties and applications, further geometric properties of functions: quasi-convex functions, their characteristics, properties and applications, unconstrained optimisation: geometric characteristics, characteristics using calculus and applications, constrained optim- 33 station with equality constraints: geometric characteristics, Lagrange characterisation using calculus and applications, properties of value function: envelope theorem and applications

Linear programming

Graphical solution, matrix formulation, duality, economic interpretation

Integration, differential equations, and difference equations

Definite integrals, indefinite integrals and economic applications, first order difference equations, equilibrium and its stability, first order differential equations, phase diagrams and stability