Contents

1. System of Linear Equation

1. Introduction

2. Elementary Transformations

3. Rank of a Matrix

4. Row Echelon Form of a Matrix

5. System of Linear Equations

5.1 Homogeneous System of Linear Equations

5.2 Non-homogeneous System of Linear Equations

6. Biological Applications on Matrices

7. Eigenvalues and Eigenvectors

7.1 Definition (Eigenvalue and Eigenvector of A)

7.2 Characteristic Matrix

7.3 Characteristic Polynomial

7.4 Characteristic Equation

7.5 Properties of Eigenvalues and Eigenvectors

7.6 Working Rule for Finding Eigenvalues and Eigenvectors

7.7 Cayley Hamilton Theorem

2. Differential Equations

1. Introduction

2. An Order and Degree of Differential Equations

3. General and Particular Solution of Differential Equations

3.1 General Solution of Differential Equation

3.2 Particular Solution of Differential Equation

4. Differential Equations of 1st Order and 1st Degree

4.1 Variable Separation Method

5. Homogeneous Differential Equations

5.1 Homogeneous Function

5.2 Homogeneous Differential Equation

6. Non-homogeneous Differential Equations

7. Applications of Differential Equations

7.1 Population Growth Problem

7.2 Decay Problems and Newton’s Law of Cooling

3. Differential Calculus

1. Introduction

2. Derivative and its Physical Significance

3. Derivative of a Function

4. Basic Rules for Differentiation and Derivatives of Some Standard

5. Implicit Function

6. Maxima and minima

7. Applications of Derivatives in Biology

8. Wave Equation

9. Heat Equation

10. Laplace Equation

4. Integral Calculus

1. Introduction

2. Integration of Functions

3. Geometric Meaning of Integration and Applications in Finding Area

4. Applications of Integration in Biology

5. Probability and Probability Distribution

1. Probability Theory Experiments

1.1 Sample Space and Events

1.2 Classical Probability

1.3 Axiomatic Approach to Probability

1.4 Conditional Probability

2. Independence of Two events

3. Discrete Random Variable

3.1 Random Variable

3.2 Discrete Random variable

3.3 Probability Distributions

3.4 Binomial Distribution

3.5 Poisson Distribution

3.6 Normal Distribution

6. Hypothesis Testing and Correlation

1. Hypothesis

1.1 Terms used in Inference

1.2 Tests of Hypothesis

1.3 Large Sample Tests

1.4 Small Sample Tests

2. ANOVA (One and Two Way)

2.1 One Way Classification

2.2 Two-way Classification

Appendix