## Topic outline

• ### General

Course Synopsis

This course introduces to the Ordinary differential equations, Laplace transform and Fourier series and their applications in solving engineering problems.

Course Outcome

i) Acquire fundamental principle of first and second order differential equations, Laplace transforms and Fourier series.

ii) Analyze and solve various first and second order differential equations, Laplace transforms and Fourier series for various periodic functions.

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• ### Topic 1

CHAPTER 1A: First Order Ordinary Differential Equations

1.1 Introduction
1.2 Basic Definitions and Terminologies
1.3 Direct Integration
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• ### Topic 2

CHAPTER 1B: First Order Ordinary Differential Equations

1.4 Homogeneous Equations
1.5 Linear Equations
1.6 Exact Equations

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• ### Topic 3

CHAPTER 2A: Second Order Ordinary Differential Equations

2.0 Introduction
2.1 Linear Homogeneous Equations
2.2 Linear Non-Homogeneous Equations      2.2.1 The Method of Undetermined Coefficients

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• ### Topic 4

CHAPTER 2B: Second Order Ordinary Differential Equations

2.2 Linear Non-Homogeneous Equations      2.2.2 The Method of Variation of Parameters
2.3 Euler Equations

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• ### Topic 5

CHAPTER 3A: Laplace Transforms

3.0 Introduction
3.1 Definition and Notation
3.2 Properties of the Laplace Transforms

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• ### Topic 6

CHAPTER 3B: Laplace Transforms

3.3 Inverse Laplace Transforms
3.4 The Convolution Theorem
3.5 Laplace Transforms of Integral

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• ### Topic 7

CHAPTER 3C: Laplace Transforms

3.6 Laplace Transforms of Derivatives
3.7 Solving ODE using Laplace Transforms
3.8 Solving Simultaneous Differential Equations

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• ### Topic 8

Chapte 4A: Fourier Series

4.0 Introduction
4.1 Periodic Function
4.2 Even and Odd Function
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• ### Topic 9

CHAPTER 4B: Fourier Series
4.3 Full Range Fourier Series
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• ### Topic 10

CHAPTER 4C: Fourier Series

4.4 Half-range Series
4.5 Effect of Harmonics

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ASSESSMENTS

1. Quiz 1

2. Quiz 2

3. Quiz 3

4. Quiz 4

5. Quiz 5

6. Quiz 6

7. Quiz 7

9. Test 1

10. Test 2

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