Syllabus
Linear Algebra
Matrices-definition, Types of matrices, Addition and subtraction of matrices, Multiplication of matrices, Properties of matrix multiplication, Transpose of a matrix, Symmetric and Skew-symmetric matrix, Orthogonal matrix, Adjoint of a matrix, Singular and Non-Singular matrix, Inverse of a matrix, Rank of a matrix, Cramer’s rule, Eigen Values and Eigen Vectors, Cayley Hamilton Theorem,
Sequence and Series Sequence-definition, Arithmetic progression, Geometric Progression, Harmonic Progression, Infinite series, Sum to infinity, Matrices, Determinants and properties of determinants, Minors and co-factors,
Basic calculus
Functions, Limits-definition problems Continuity-definition, properties, Continuity on an interval and continuity of polynomials, continuity of rational functions Differentiation- Slopes and Rate of change Product rule, Quotient rule Derivative of rational powers of x, Implicit differentiation Indeterminate forms and L Hospital rule Integration – Indefinite integral Integration from the view point of differential equations, Integration by substitution, Area as a limit of a sum, The definite integral,
Differential Equation
Differential Equations Definition, Initial and boundary value problems, Classification of First order differential equations, Linear equations, Bernoulli’s equation, Exact equations Separable equations, Homogeneous equations,
Statistics
Statistics, Collection, Classification and Tabulation of data, Bar diagrams and Pie diagrams, Histogram, Frequency curve and frequency polygon, Ogives Mean, median,mode, Standard deviation.
Lecture by lecture details
| Lecture number |
Topics |
Objectives |
Remarks |
| 1 |
Matrices-definition, Types of matrices, Addition and subtraction of matrices |
|
|
| 2 |
Multiplication of matrices, Properties of matrix multiplication |
|
|
| 3 |
Determinants and properties of determinants, Minors and co-factors |
|
|
|
Transpose of a matrix, Symmetric and Skew- symmetric matrix, Orthogonal matrix |
|
|
| 5 |
Adjoint of a matrix, Singular and Non-Singular matrix, Inverse of a matrix |
|
|
| 6 |
Cramer’s rule |
Use vectors and matrices to solve linear systems of algebraic euqations. |
|
| 7 – 8 |
Rank of a matrix |
|
|
| 9 |
Eigen Values and Eigen Vectors
|
Find the eigenvalues and eigenvectors of a matrix. |
|
| 10 |
Cayley Hamilton Theorem |
|
|
| 11 – 13 |
Arithmetic progression, Geometric Progression, Harmonic Progression |
|
|
| 14 |
Functions, Limits-definition problems Continuity-definition, properties |
Basic Concepts |
|
| 15-16 |
Continuity on an interval and continuity of polynomials, continuity of rational functions |
|
| 17-18 |
Differentiation- Slopes and Rate of change, Product rule Quotient rule |
|
| 19-20 |
Derivative of rational powers of x, Implicit differentiation Indeterminate forms and L Hospital rule |
|
| 21-22 |
Integration – Indefinite integral Integration from the view point of differential equations |
|
| 23 – 24 |
Integration by substitution Area as a limit of a sum The definite integral, |
|
|
| 25- 27 |
Differential Equations Definition, Initial and boundary value problems |
Know what is meant by a “differential equation.” Determine if a given function is a solution to a particular differential equation.
Understand how the terms linear, non-linear, order, ordinary and partial are used to classify differential equations. Find all solutions of a separable differential equation. Find the general solution to a linear first order differential equation. Find the general solution for a first order, linear, constant coefficient, homogeneous system of differential equations. |
|
| 28 |
Classification of First order differential equations, Linear equations |
|
|
| 29-30 |
Bernoulli’s equation |
|
|
| 31 – 32 |
Exact equations Separable equations |
|
|
| 33 -35 |
Homogeneous equations |
|
|
| 36 – 38 |
Statistics, Collection, Classification and tabulation of data |
|
|
| 39 -40 |
Bar diagrams and Pie diagrams, |
|
|
| 40 – 42 |
Histogram, Frequency curve and frequency polygon, Ogives |
|
|
| 43 |
Measures in central tendency Measures of dispersion |
|
|
| 44-45 |
Problem solving |
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