## Understanding Calculus By: Faraz Hussain

Duke University ’98

BS Civil Engineering , Minor English

University of Illinois – Urbana Champaign ’00

MS Structural Engineering

Copyright 2007 – Faraz Hussain

All Rights Reserved

### Table of Contents

### Part 1

##### Preface

##### Chapter 1 – Why Study Calculus?

##### Chapter 2 – Understanding Numbers

- Section 2.1 – Numbers and their Uses
- Section 2.2 – Interpreting Numbers
- Section 2.3 – Risk Assessment

##### Chapter 3 – The Mathematical function and its Graph

- Section 3.1 – The Scientific Method
- Section 3.2 – Nonsense Detection – The UnScientific Method
- Section 3.3 – Dimensions
- Section 3.4 – The Mathematical Function
- Section 3.5 – Two Dimensional Functions
- Section 3.6 – The Graph of a Function

##### Chapter 4 – The Derivative

- Section 4.1 – Rate of Change
- Section 4.2 – Average Rate of Change
- Section 4.3 – Instantaneous Rate of Change
- Section 4.4 – The Derivative

##### Chapter 5 – Differentiating Functions

- Section 5.1 – Differentiating Functions
- Section 5.2 – Differentiating Sums of Functions
- Section 5.3 – Differentiating Products of Functions
- Section 5.4 – Differentiating Functions of any Power of N
- Section 5.5 – Differentiating Functions of Functions

##### Chapter 6 – Applications of the Derivative

- Section 6.1 – Motion, Velocity and Acceleration
- Section 6.2 – Instantaneous Velocity and Acceleration

##### Chapter 7 – Study of Free Falling Bodies

- Section 7.1 – What is a Force?
- Section 7.2 – Understanding Free-Fall Motion
- Section 7.3 – Initial Conditions for Motion

##### Chapter 8 – Understanding the Derivative

- Section 8.1 – Using the First Derivative
- Section 8.2 – Using the Second Derivative
- Section 8.3 – The Systematic Use of the Derivatives

##### Chapter 9 – The Derivative and its Approximations

##### Chapter 10 – Theory of Integration

##### Chapter 11 – Understanding Integration

- Section 11.1 – Understanding Integration
- Section 11.2 – Geometric Applications
- Section 11.3 – The Systematic Approach to Integration
- Section 11.4 – Engineering Applications
- Section 11.5 – Human Applications