APPROXIMATE SCHEDULE FOR CHAPTER COVERAGE
Chapter |
Topics.
Suggested Exercises |
Approx.No. of Weeks |
1 |
CHAPTER PREREQUISITES AND page 343 |
2 |
1 |
|
2.5 - 3 |
2 |
DIFFERENTIATION
|
4 -- 4.5 |
3 |
APPLICATIONS
OF DIFFERENTIATION
|
2.5 -- 3 |
5 |
TRANSCENDETAL FUNCTIONS
|
2 -- 2.5 |
|
Antiderivatives / Indefinite Integrals A tutorial on antiderivatives and indefinite integrals. Covers the Uniqueness Theorem, inverse property and applications of indefinite integrals. · Table of Elementary Indefinite Integrals ·
An example illustrating the evaluation of an
indefinite integral using properties of indefinite integrals. ·
Drill on evaluating simple integrals using the Table
of Elementary Integrals. ·
Drill on evaluating simple integrals with initial
conditions. ·
Application of indefinite integrals. ·
Another application of indefinite integrals. A tutorial on slope fields with an interactive JAVA applet to explore slope fields. · A computer program that graphs the slope field for a function. · Another computer program that graphs the slope field for a function and graphs antiderivatives. · An animation illustrating the different solutions for indefinite integrals using slope fields. ·
Using a TI-86 graphing calculator to graph slope
fields and the antiderivative of a function. · TI-85 graphing calculator programs to graph slope fields. Areas A tutorial on how to find areas and approximation to areas by using inscribed and circumscribed rectangles. · An animation illustrating the approximation of the area under the sine function by inscribed and circumscribed rectangles. · An animation illustrating the approximation of the area under a parabola by inscribed and circumscribed rectangles. · A computer program that illustrates the approximation of the area of a circle using inscribed polygons. · An animation showing the approximation of the area of a circle using inscribed polygons. · A computer program that graphically illustrates the Monte Carlo Method to find areas. Riemann Sums A tutorial on riemann sums from the graphical point of view followed by a tutorial from a symbolic or algebraic point of view. · A tutorial on summations and summation notation. · An example of a sum evaluated using the TI-85 or TI-86 graphing calculator. · Another example of a sum evaluated using the TI-85 or TI-86 graphing calculator. · Using a graphing calculator to evaluate Riemann Sums. · Computer software that graphically illustrates the use of Riemann sums to approximate the area bounded by the graph of a function and the x-axis and a couple of lines. · Computer software that graphically and numerically approximate an area. · Computer software that graphically and numerically approximate an area by evaluating upper and lower Riemann sums. Definite Integrals A tutorial on the definition of definite integrals, properties of definite integrals, relationship between definite integrals and areas and the use of technology to evaluate definite integrals using the definition. ·
A Flash movie illustrating the evaluation of a
definite integral using the definition. · A Flash movie illustrating the finding the area by using the definition of a definite integral. · Using a computer algebra system and Riemann sums to evaluate definite integrals. · Computer software that can symbolically evaluate an integral using Riemann Sums. Fundamental Theorem of Calculus Tutorial on the Fundamental Theorem of Calculus. · Examples illustrating use of the Fundamental Theorem of Calculus to evaluate definite integrals. ·
Drill problems on evaluating definite integrals using
the Fundamental Theorem of Calculus. · A interactive Java applet to graphically illustrate the Fundamental Theorem of Calculus. ·
An animation illustrating the Fundamental Theorem of
Calculus. · Using the graphing calculator to illustrate graphically the Fundamental Theorem of Calculus. · A Maple animation illustrating graphically the Fundamental Theorem of Calculus. · Computer programs that graphically illustrate the Fundamental Theorem of Calculus. · Computer algebra systems and to what extent does Maple "knows" the Fundamental Theorem of Calculus. Techniques of Integration - Substitution Tutorial on integration using the method of substitution. · Drill problems for integration using the method of substitution. · Quiz on substitutions and elementary integrals. ·
Drill on evaluating certain integrals. · Drill problems for integration using the method of trigonometric substitution. · Using Maple to illustrate the method of substitution. Techniques of Integration - Integration by Parts Tutorial on using Integration by Parts. ·
Some drill problems using Integration by Parts. ·
Some drill problems using Integration by Parts. · Some more drill problems using Integration by Parts. · Derivation of Integration by Parts formula (uses dynamic html). · Using Maple to illustrate the method of Integration by Parts. Techniques of Integration - Reduction Formulas Tutorial on deriving and using recursion or reduction formulas. · Drill problems for evaluating trigonometric integrals using recursion or reduction formulas. · Using Maple to obtain some reduction formulas. Techniques of Integration - Partial Fractions Tutorial on the method of Partial Fractions. · Examples illustrating the the method of Partial Fractions. ·
Some drill problems · Drill problems for integration using the method of Partial Fractions. Techniques of Integration · Using Maple to evaluate indefinite integrals. Numerical Integration Tutorial on numerical integration. · An animation illustrating graphically the Trapezoidal Rule. · Using a graphing calculator to illustrate the use of the Trapezoidal Rule. · Computer programs that graphically illustrate the use of the Trapezoidal Rule. · An animation illustrating graphically Simpson's Rule. · Using a graphing calculator to illustrate the use of the Simpson's Rule. · Computer programs that graphically illustrate the use of Simpson's Rule. · Computer programs that numerically illustrate the use of Simpson's Rule. · TI-85 graphing calculator programs for numerical integration. · Computer programs that provide a graphical illustration of the Midpoint Rule. Tutorial on numerical integration and error bounds. Improper Integrals Tutorial on improper integrals over unbounded intervals. · Drill problems on evaluating improper integrals over unbounded intervals. [Using Java] Drill problems on evaluating improper integrals over unbounded intervals. Tutorial on improper integrals of functions with discontinuities. |
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* This schedule is subject to change for the optimum benefit of the class as a whole. Therefore it is important to stay alert and attend class regularly.