The word Calculus derived from the Latin word meaning “small stone”.
Calculus, a branch of mathematics deals with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus).
Calculus is the one approach which makes possible to solve problems as diverse like tracking the position of a space shuttle or calculating the pressure building up behind a dam as the water rises.
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Table of Content – “Gilbert Strang Calculus Book Pdf”
1. Introduction to Calculus
- Velocity and Distance
- Calculus Without Limits
- The Velocity at an Instant
- Circular Motion
- A Review of Trigonometry
- A Thousand Points of Light
- Computing in Calculus
- The Derivative of a Function
- Powers and Polynomials
- The Slope and the Tangent Line
- The derivative of the Sine and Cosine
- The Product and Quotient and Power Rules
- Continuous Functions
3. Applications of the Derivative
- Linear Approximation
- Maximum and Minimum Problems
- Second Derivatives: Minimum vs. Maximum
- Ellipses, Parabolas, and Hyperbolas
- Iterations x,+ ,= F(x,)
- Newton’s Method and Chaos
- The Mean Value Theorem and l’H8pital’s
4. The Chain Rule
- Derivatives by the Chain Rule
- Implicit Differentiation and Related Rates
- Inverse Functions and Their Derivatives
- Inverses of Trigonometric Functions
- The Idea of the Integral
- Summation vs. Integration
- Indefinite Integrals and Substitutions
- The Definite Integral
- Properties of the Integral and the Average Value
- The Fundamental Theorem and Its Consequences
- Numerical Integration
6. Exponential and Logarithms
- An Overview
- The Exponential ex
- Growth and Decay in Science and Economics
- Separable Equations Including the Logistic Equation
- Powers Instead of Exponentials
- Hyperbolic Functions
7. Techniques of Integration
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitutions
- Partial Fractions
- Improper Integrals
8. Applications of the Integral
- Areas and Volumes by Slices
- Length of a Plane Curve
- Area of a Surface of Revolution
- Probability and Calculus
- Masses and Moments
- Force, Work, and Energy
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