APPROXIMATE SCHEDULE FOR CHAPTER COVERAGE

Chapter

Topics. Suggested Exercises

Approx.No. of Weeks

1

CHAPTER PREREQUISITES AND page 343

 

2

1

LIMITS AND THEIR PROPERTIES

  • 1.1 A Preview to Calculus
  • 1.2 An Introduction to Limits, Exercises: pp. 78-79, # 1-31, 33-34, 41
  • 1.3 Properties of Limits , Exercises: pp. 84-85, # 1-32, 35
  • 1.4 Techniques for Evaluating Limits , Exercises: pp. 92-93, # 1-42, 55, 56
  • 1.5 Continuity and One-sided Limits , Exercises: pp. 102-105, # 1-60
  • 1.6 Infinite Limits , Exercises: pp. 111-112, #1-42, 45-58

2.5 - 3

Quiz 1
Quiz 1
Quiz 1

2

DIFFERENTIATION
For sections 2.1-2.6, do all exercises except those marked "C."

  • 2.1 The Derivative and the Tangent Line Problem
  • 2.2 Basic Differentiation Rules and Rates of Change
  • 2.3 The Product and Quotient Rules and Higher Order Derivatives (Sec. 2.3)
  • 2.4 The Chain Rule
  • 4.7 Logarithmic Differentiation ( pp. 328], Exercises: pp. 330-331, # 3-21, 25-30, 35-41
  • 2.5 Implicit Differentiation
  • 2.6 Related Rates

4 -- 4.5

Quiz 1
Formulas

3

APPLICATIONS OF DIFFERENTIATION
For sections 3.1, 3.4, 3.6, do all exercises except those marked "C."

  • 3.1 Extrema on an Interval
  • 3.2 Rolle's Theorem and the Mean Value Theorem Exercises: Optional
  • 3.3 Increasing and Decreasing Functions , the First Derivative Test Exercises: pp. 198-200, #1-32,37-46, 48-52, 55-65. For #21-32, omit confirmation of results with a graphing tool.
  • 3.4 Concavity and the Second Derivative Test
  • 3.5 Limits at Infinity , Exercises: pp. 215-216, # 1-48, 59-62, 64-73
  • 3.6 A Summary of Curve Sketching
  • 3.7 Optimization Problems , Exercises: pp. 230-234, # 1-25, 27-56, 59, 60. Omit 1d, 1e, 19d, 33d, 33e, 56d,56e

2.5 -- 3

Quiz 1
Quiz 1
Quiz 1

5

TRANSCENDETAL FUNCTIONS

  • 5.2 Differentiation of Logarithmic Functions with Bases Other Than e , Exercises: pp.348-350, # 1-40,, 72-77
  • 5.5 Inverse Trigonometric functions , Exercises: pp. 377-378, #1-10, 11-27
  • 5.7 Hyperbolic functions , Exercises: pp.396-397, #1-28, 51-58.

2 -- 2.5

 

INTEGRATION

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.
[using Flash]

·         Drill on evaluating simple integrals using the Table of Elementary Integrals.
[Using Java]

·         Drill on evaluating simple integrals with initial conditions.
[Using Java]  

·         Application of indefinite integrals.
[using Flash]

·         Another application of indefinite integrals.
[using Flash]

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.
[using Flash]

·         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.
[using Flash] [using Java]

·         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.
[Using Java]

·         A interactive Java applet to graphically illustrate the Fundamental Theorem of Calculus.

·         An animation illustrating the Fundamental Theorem of Calculus.
[Using animated gifs]

·         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.
[Using Java]

·         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.
[Using Java]

·         Some drill problems using Integration by Parts.
[Using Java]Some drill problems using Integration by Parts.
[Using Java]

·          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
[Using Java]

·         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.

 

 

 

 

 

 

 

* 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.