Calculus Problems for a New Century: Resources for Calculus Collection : A Project of the Associated Colleges of the Midwest and the Great Lakes Col (M A A NOTES)

Calculus Problems for a New Century Emphasizes conceptual understanding over rote drill. The problems are organized in groups that parallel traditional grouping of ideas, making it possible to use them as supplements to most texts. Most of the problems can be done without the use of a calculator or computer. Cover Title Page MAA Notes and Reports Series Copyright Introduction: Resources for Calculus Collection The Five Volumes of the Resources for Calculus Collection Acknowledgements Table of Contents Foreword Acknowledgements for Volume II Suggestions to the Student Suggestions to the Instructor Chapter I. Functions and Graphs 1. Domain and Range. Elementary Functions 2. Trigonometric Functions 3. Exponential and Logarithmic Functions 4. Composite Functions 5. Functions Described by Tables or Graphs 6. Parametric Equations 7. Polar Coordinates Chapter II. The Derivative 1. Average Rates of Change 2. Introduction to the Derivative 3. Graphical Differentiation Problems 4. Limits 5. Continuity 6. Power, Sum and Product Rules 7. The Chain Rule 8. Implicit Differentiation and Derivatives of Inverses 9. Derivatives of Trigonometric, Log, and Exponential Functions 10. Root Finding Methods 11. Related Rates Chapter III. Extreme Values 1. Increasing and Decreasing Functions and Relative Extrema 2. Concavity and the Second Derivative 3. Max-Min Story Problems Chapter IV. Antiderivatives and Differential Equations 1. Antiderivatives 2. Introduction to Differential Equations Chapter V. The Definite Integral 1. Riemann Sums 2. Properties of Integrals 3. Geometric Integrals 4. The Fundamental Theorem of Calculus 5. Functions Defined by Integrals Chapter VI. The Definite Integral Revisited 1. Exact Values from the Fundamental Theorem of Calculus 2. Techniques of Integration 3. Approximation Techniques and Error Analysis Chapter VII. Sequences and Series of Numbers 1. Sequences of Numbers 2. Series of Numbers. Geometric Series 3. Convergence Tests: Positive Series 4. Convergence Tests: All Series 5. Newton's Method 6. Improper Integrals Chapter VIII. Sequences and Series of Functions 1. Sequences of Functions. Taylor Polynomials 2. Series of Functions. Taylor Series 3. Power Series Chapter IX. The Integral in IR2 and IR3 1. Real-valued Functions of Two and Three Variables 2. Definition of Double and Triple Integrals 3. Evaluation of Double Integrals Chapter X. Vectors and Vector Geometry 1. Vectors 2. Velocity and Acceleration 3. Arc Length Chapter XI. The Derivative in Two and Three Variables 1. Partial Derivatives 2. Gradient and Directional Derivatives 3. Equation of the Tangent Plane 4. Optimization Chapter XII. Line Integrals 1. Line Integrals 2. Conservative Vector Fields and Green's Theorem Chapter I. Functions and Graphs 1. Domain and Range. Elementary Functions 2. Trigonometric Functions 3. Exponential and Logarithmic Functions 4. Composite Functions 5. Functions Described by Tables or Graphs 6. Parametric Equations 7. Polar Coordinates Chapter II. The Derivative 1. Average Rates of Change 2. Introduction to the Derivative 3. Graphical Differentiation Problems 4. Limits 5. Continuity 6. Power, Sum and Product Rules 7. The Chain Rule 8. Implicit Differentiation and Derivatives of Inverses 9. Derivatives of Trigonometric, Log, and Exponential Functions 10. Root Finding Methods 11. Related Rates Chapter III. Extreme Values 1. Increasing and Decreasing Functions and Relative Extrema 2. Concavity and the Second Derivative 3. Max-Min Story Problems Chapter IV. Antiderivatives and Differential Equations 1. Antiderivatives 2. Introduction to Differential Equations Chapter V. The Definite Integral 1. Riemann Sums 2. Properties of Integrals 3. Geometric Integrals 4. The Fundamental Theorem of Calculus 5 . Functions Defined by Integrals Chapter VI. The Definite Integral Revisited 1. Exact Values from the Fundamental Theorem of Calculus 2. Techniques of Integration 3. Approximation Techniques and Error Analysis Chapter VII. Sequences and Series of Numbers 1. Sequences of Numbers 2. Series of Numbers. Geometric Series 3. Convergence Tests: Positive Series 4. Convergence Tests: All Series 5. Newton's Method 6. Improper Integrals Chapter VIII. Sequences and Series of Functions 1. Sequences of Functions. Taylor Polynomials 2. Series of Functions. Taylor Series 3. Power Series Chapter IX. The Integral in IR2 and IR3 1. Real-valued Functions of Two and Three Variables 2. Definition of Double and Triple Integrals 3. Evaluation of Double Integrals Chapter X. Vectors and Vector Geometry 1. Vectors 2. Velocity and Acceleration 3. Arc Length Chapter XI. The Derivative in Two and Three Variables 1. Partial Derivative 2. Gradient and Directional Derivatives 3. Equation of the Tangent Plane 4. Optimization Chapter XII. Line Integrals 1. Line Integrals 2. Conservative Vector Fields and Green's Theorem

even In Our Age Of Calculators And Computers, We Still Need Problems That Will Help Students Develop Fundamental Skills And Give Them A Sense Of Progress In Their Study. These Problems Must Be Phrased Differently, However, Than The Traditional Lists Of The Past. At The Very Least, They Cannot Be Rendered Trivial By Available Electronic Aids; At Best They Should Make Use Of Such Aids To Lead The Student To Greater Understanding.

this Volume Contains Problems Written With These Objectives In Mind. The Authors Have Tried To Emphasize Conceptual Understanding Over Rote Drill. Although Many Of The Problems Require The Use Of A Calculator Or Computer Algebra System, Most Do Not. A Deliberate Effort Has Been Made To Stress Graphs And Tables, Rather Than Rules To Define Function, In The Belief That Real World Data Generally Come That Way.

the Problems Are Organized In Groups That Parallel Traditional Grouping Of Ideas, Making It Possible To Use Them As Supplements To Most Texts. All Of The Problems Are Given With Commentaries That Frequently Give A Bit Of History About The Problem, As Well As Show How The Question Can Be Extended And Viewed In A Different Context. Our Aim Is To Provide Teachers With Problems And Exercises To Challenge The Current Calculus Student.

the Mathematics Teacher - Connie Buller

this Book Should Be A Boon To New Teachers Of Calculus Who Don't Already Have A Stockpile Of Great Questions And Hate To Use Only The Examples Presented In Their Particular Textbook.

"Faculty members in most disciplines provide students in beginning courses with some history of their subject, some sense not only of what was done by whom, but also of how the discipline has contributed to intellectual history. These essays, appropriate for duplicating and handing out as collateral reading aim to provide such background, and also to develop an understanding of how mathematicians view their discipline."--Page x v. 1. Learning by discovery : a lab manual for calculus / Anita E. Solow, editor v. 2 Calculus problems for a new century / Robert Fraga, editor v. 3. Applications of calculus / Philip Straffin, editor v. 4. Problems for student investigation / Michael B. Jackson and John R. Ramsay, editors v. 5. Readings for calculus / Underwood Dudley, editor Beginning with a conference at Tulane University in January, 1986, there developed in the mathematics community a sense that calculus was not being taught in a way befitting a subject that was at once the culmination of the secondary mathematics curriculum and the gateway to collegiate science and mathematics. "A Project of the Associated Colleges of the Midwest and the Great Lakes Colleges Association."