Understanding Calculus

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
Chapter 3 – The Mathematical function and its Graph
Chapter 4 – The Derivative
Chapter 5 – Differentiating Functions
Chapter 6 – Applications of the Derivative
Chapter 7 – Study of Free Falling Bodies
Chapter 8 – Understanding the Derivative
Chapter 9 – The Derivative and its Approximations
Chapter 10 – Theory of Integration
Chapter 11 – Understanding Integration
Chapter 12 – Differentials

Part 2

Chapter 13 – Inverse Functions
Chapter 14 – Introduction to Exponents
Chapter 15 – Logarithmic and Exponential Functions
Chapter 16 – Applications of the Exponential Function
Chapter 17 – The Sine and Cosine Function
Chapter 18 – The Sine Function – Definition
Chapter 19 – Differentiating and Integrating the Sine function
Chapter 20 – Applications of the Sine Function – Oscillatory Motion
Chapter 21 – The Mean Value Theorem
Chapter 22 – Taylor Series
Chapter 23 – More on Taylor Series
Chapter 24 – Techniques of Integration

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