Insights into Calculus Using MAPLE V

by Smith, Robert T.; Minton, Roland B.; Duchrow, Linda; Calvis, David

• ISBN13: 9780072374698
• ISBN10: 0072374691
• Edition: 1st
• Format: Paperback
• Copyright: 1999-10-07
• Publisher: McGraw-Hill Higher Education

Table of Contents

Expressions and Functions (0.1&2)	1	(3)
Arithmetic operations; entering and evaluating expressions and functions
Graphing Functions (0.3)	3	(2)
Graphing functions; specifying the viewing window; graphing two functions together
Solving Equations (0.4)	5	(2)
Algebraic and numerical equation solving; other algebraic operations
Trigonometry and Exponentials (0.5&6)	7	(2)
Trigonometric, exponential and logarithmic functions; the constants e and π
Limits, Part I (1.1)	9	(2)
Finding two-and one-sided limits of functions of one variable
Limits, Part II (1.4)	11	(2)
Limits involving infinity
Limits, Part III (1.6)	13	(2)
Loss of significance errors; scientific notation
Derivatives of Explicit Functions (2.1-7)	15	(2)
Finding first derivatives by definition; finding derivatives symbolically
Implicit Differentiation (2.8)	17	(2)
Plotting and finding derivatives for implicity-defined curves
Newton's Method (3.1)	19	(2)
Applying Newton's method; dependence of Newton's method upon starting point
Curve Sketching (3.5)	21	(2)
Curve sketching; using derivative plots to find critical points
Integration and Riemann Sums (4.1-4)	23	(2)
Indefinite and definite integrals; evaluating Riemann sums
Numerical Integration (4.7)	25	(2)
Midpoint, Trapezoid and Simpson's Rules; numerical integration
Solids of Revolution (5.1-4)	27	(2)
Drawing and experimenting with solids of revolution; volume and surface area
Probability (5.7)	29	(2)
Random trials and histograms
Separable Differential Equations (6.5)	31	(2)
Solving separable differential equations; graphing particular and general solutions
Euler's Method (6.6)	33	(2)
Direction fields; applying and graphing Euler's method
Integration Techniques (7.1-5)	35	(2)
Finding antiderivatives; checking answers; exceptional situations
Improper Integrals (7.7)	37	(2)
Discontinuous integrands; infinite limits of integration
Infinite Series (8.2-7)	39	(2)
Series of constants; finding and graphing Taylor series
Fourier Series (8.8)	41	(2)
Finding and graphing Fourier series; the Gibbs phenomenon
Parametric Equations (9.1-3)	43	(2)
Graphing parametric curves; calculus with parametric equations
Polar Coordinates (9.4-7)	45	(2)
Graphing in polar coordinates; calculus with polar coordinates
Vectors (10.1-5)	47	(2)
Vectors in two and three dimensions; vector operations and graphing vectors
Vector-Valued Functions, Part I (11.1-3)	49	(2)
Graphing vector-valued functions in the plane; derivatives and reparameterization
Vector-Valued Functions, Part II (11.1-4)	51	(2)
Arc length and curvature; vector-valued functions in space
Functions of Two Variables (12.1-2)	53	(2)
Graphing functions of two variables; contour and density plots; limits
Partial Derivatives (12.3-7)	55	(2)
Functions of three variables; finding partial derivatives; gradients and local extrema
Double Integrals (13.1-3)	57	(2)
Evaluating double integrals; Riemann sums; polar coordinates
Triple Integrals (13.4-7)	59	(2)
Surface area; evaluating triple integrals; cylindrical and spherical coordinates
Vector Fields in the Plane (14.1-4)	61	(2)
Plotting plane vector fields and flow lines; gradient fields;Green's Theorem
Vector Fields in Space (14.6-8)	63	(2)
Parametrically-defined surfaces; space vector fields; flux integrals, divergence and curl; Stoke's Theorem
Index of Maple V Commands and Options	65
Page of First Use and Pages For Additional Information