Computing for Calculus

1st Edition - January 1, 1981
Author: Mark J. Christensen
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 7 1 0 8 - 8

Computing for Calculus focuses on BASIC as the computer language used for solving calculus problems. This book discusses the input statement for numeric variables, advanced… Read more

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Computing for Calculus focuses on BASIC as the computer language used for solving calculus problems. This book discusses the input statement for numeric variables, advanced intrinsic functions, numerical estimation of limits, and linear approximations and tangents. The elementary estimation of areas, numerical and string arrays, line drawing algorithms, and bisection and secant method are also elaborated. This text likewise covers the implicit functions and differentiation, upper and lower rectangular estimates, Simpson's rule and parabolic approximation, and interpolating polynomials. Other topics include the Taylor polynomials, estimating the limit of a sequence, infinite series, and level curves and central projection of surfaces. This publication is beneficial to math students and specialists who use computer languages for educational purposes.

Chapter 1 Basic BASIC

1.1 The Language BASIC

1.2 The Structure of a Computer Program

1.3 Numeric Variables

1.4 Printing Numeric Variables

Exercises

1.5 The INPUT Statement for Numeric Variables

Exercises

1.6 Printing String Constants

Exercises

1.7 String Variables

Exercises

1.8 The FOR-NEXT Statement: Looping

Exercises

1.9 The Intrinsic Functions

Exercises

1.10 Advanced Intrinsic Functions

Exercises

1.11 User Defined Functions

Exercises

1.12 The IF and GOTO Statements

Exercises

1.13 The GOSUB Statement

Exercises

Chapter 2 Estimation Of Derivatives

2.1 Printing Tables of Functions

Exercises

2.2 Numerical Estimation of the First Derivative

Exercises

2.3 Numerical Estimation of Limits

Exercises

2.4 Linear Approximations and Tangents

Exercises

Chapter 3 The Definite Integral

3.1 Elementary Estimation of Areas

Exercises

Chapter 4 Graphics

4.1 Elementary Graphics

Exercises

4.2 Numerical and String Arrays

Exercises

4.3 Line Drawing Algorithms

Exercises

4.4 Polar Graphing

Exercises

Chapter 5 Solving Equations

5.1 The Bisection Method

Exercises

5.2 The Secant Method

Exercises

5.3 Newton's Methods

Exercises

Chapter 6 Implicit Functions And Differentiation

6.1 Implicit Functions

Exercises

6.2 Implicit Differentiation

Exercises

Chapter 7 Estimation Of Areas Revisited

7.1 Upper and Lower Rectangular Estimates

Exercises

7.2 The Trapezoidal Rule

Exercises

7.3 Simpson's Rule and Parabolic Approximation

Exercises

Chapter 8 Approximation Of Functions

8.1 Interpolating Polynomials

Exercises

8.2 Taylor Polynomials

Exercises

Chapter 9 Estimation Of Sequences And Series

9.1 Estimating the Limit of a Sequence

Exercises

9.2 Infinite Series

Exercises

Chapter 10 Three-Dimensional Graphics

10.1 Level Curves of a Surface

Exercises

10.2 The Central Projection of Surfaces

Exercises