Resequencing Calculus: Dwyer and Gruenwald Definition Resequencing Calculus: Rationale An Early Multivariate Approach Text Piloting Challenges David Dwyer and Mark Gruenwald Solutions University of Evansville Further Information January 4, 2012 Supported by NSF Grant 0836676
What is Early Multivariate Calculus? Resequencing Calculus: Dwyer and Gruenwald Definition A reformulation of the standard 3-semester calculus Rationale sequence in which Text Vectors, matrices, functions of several variables, Piloting double (but not triple) integrals are introduced in Challenges Solutions Calculus II. Further Information Infinite series is moved to Calculus III. Other minor changes are made to ensure balancing of material across semesters.
Rationale Resequencing Calculus: Dwyer and Gruenwald Calculus II is a better jumping off point for some Definition students in Biology, Chemistry, and Economics. Rationale Text Natural progression of difficulty through the Piloting sequence Challenges Prerequisites lowered to Calculus II for Solutions calculus-based probability, linear algebra, and Further Information differential equations. Facilitates complete treatment of vector calculus in Calculus III through Stokes’ Theorem and the Divergence Theorem.
Calculus—An Early Multivariate Approach Resequencing Calculus: Coverage of resequenced Calculus I and II (11 Dwyer and Gruenwald chapters) Definition Extensive (700 pages, 1000 graphics, 2000 exercises) Rationale Discipline-specific projects Text Piloting Challenges Solutions Further Information
Calculus—An Early Multivariate Approach Resequencing Calculus: Coverage of resequenced Calculus I and II (11 Dwyer and Gruenwald chapters) Definition Extensive (700 pages, 1000 graphics, 2000 exercises) Rationale Discipline-specific projects Text Piloting Challenges Solutions Further Information
Piloting at Evansville Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Entire sequence taught at UE by multiple faculty Text members Piloting New text used for Calculus I and II Challenges Solutions Parts of Stewart’s Early Transcendentals used for Further Information Calculus III Assessment supports viability of sequence
Challenges Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Using parts of an existing text for Calculus III Text Placement of students with dual, transfer, or AP-BC Piloting credit Challenges Solutions Systemic entrenchment of existing system Further Information Translating success at Evansville into workable model at other institutions
Solutions Resequencing Calculus: Dwyer and Gruenwald Definition Expand text to include Calculus III Rationale Text Pilot sequence at other institutions Piloting Develop online multivariate modules to assist with Challenges placement of AP-BC and transfer students Solutions Develop evidence to support institutional change Further Information Work with MAA, AMATYC, and the AP to effect change
Further Information Resequencing Calculus: Dwyer and Gruenwald Definition Rationale Text Piloting Mark Gruenwald mg3@evansville.edu Challenges David Dwyer dd4@evansville.edu Solutions Further Information Website resequencingcalculus.com
Chapter 1 - Functions Resequencing Calculus: Dwyer and Gruenwald Table of Contents Chapter 1 Chapter 2 1.1 Functions and Their Graphs Chapter 3 Chapter 4 1.2 Algebra of Functions Chapter 5 Chapter 6 Chapter 7 1.3 Library of Functions Chapter 8 Chapter 9 1.4 Implicit Functions and Conic Sections Chapter 10 Chapter 11 Chapter 12 1.5 Polar Functions Chapter 13 Chapter 14 1.6 Parametric Functions Chapter 15 Chapter 16 Revised Sequence
Chapter 2 - Limits Resequencing Calculus: Dwyer and Gruenwald Table of Contents Chapter 1 Chapter 2 2.1 Limits in Calculus Chapter 3 Chapter 4 2.2 Limits: Numerical and Graphical Approaches Chapter 5 Chapter 6 Chapter 7 2.3 Calculating Limits Using Limit Laws Chapter 8 Chapter 9 2.4 Limits at Infinity and Horizontal Asymptotes Chapter 10 Chapter 11 Chapter 12 2.5 Continuity and the Intermediate Value Theorem Chapter 13 Chapter 14 2.6 The Precise Definition of a Limit Chapter 15 Chapter 16 Revised Sequence
Chapter 3 - The Derivative Resequencing Calculus: Dwyer and Gruenwald 3.1 Tangents, Velocities, and Other Rates of Change Table of Contents 3.2 Derivatives Chapter 1 Chapter 2 Chapter 3 3.3 Rules for Differentiation Chapter 4 Chapter 5 3.4 Product and Quotient Rules Chapter 6 Chapter 7 3.5 Trigonometric Functions and Their Derivatives Chapter 8 Chapter 9 Chapter 10 3.6 Chain Rule Chapter 11 Chapter 12 3.7 Parametric and Polar Differentiation Chapter 13 Chapter 14 Chapter 15 3.8 Implicit Differentiation Chapter 16 Revised Sequence 3.9 Inverse Functions and Their Derivatives 3.10 Logarithmic Functions and Their Derivatives
Chapter 4 - Applications of the Derivative Resequencing Calculus: Dwyer and Gruenwald 4.1 Maximum and Minimum Values Table of Contents Chapter 1 4.2 The Mean Value Theorem Chapter 2 Chapter 3 Chapter 4 4.3 Derivatives and Graphs Chapter 5 Chapter 6 4.4 Optimization Chapter 7 Chapter 8 Chapter 9 4.5 Applications to Rates of Change Chapter 10 Chapter 11 4.6 Indeterminate Limits and L’Hopital’s Rule Chapter 12 Chapter 13 Chapter 14 4.7 Polynomial Approximations Chapter 15 Chapter 16 4.8 Tangent Line Approximations: Differentials and Revised Sequence Newton’s Method
Chapter 5 - The Integral Resequencing Calculus: Dwyer and Gruenwald Table of Contents Chapter 1 Chapter 2 Chapter 3 5.1 Antiderivatives and Indefinite Integrals Chapter 4 Chapter 5 5.2 Area Under a Curve and Total Change Chapter 6 Chapter 7 5.3 The Definite Integral Chapter 8 Chapter 9 Chapter 10 5.4 The Fundamental Theorem of Calculus Chapter 11 Chapter 12 5.5 Integration By Substitution Chapter 13 Chapter 14 Chapter 15 Chapter 16 Revised Sequence
Chapter 6 - Techniques of Integration Resequencing Calculus: Dwyer and Gruenwald Table of Contents Chapter 1 Chapter 2 Chapter 3 6.1 Advanced Substitution techniques Chapter 4 Chapter 5 6.2 Integration by Parts Chapter 6 Chapter 7 6.3 Integrating Rational Functions Chapter 8 Chapter 9 Chapter 10 6.4 Improper Integrals Chapter 11 Chapter 12 6.5 Approximating Definite Integrals Chapter 13 Chapter 14 Chapter 15 Chapter 16 Revised Sequence
Chapter 7 - Applications of Integration Resequencing Calculus: Dwyer and Gruenwald Table of Contents Chapter 1 Chapter 2 7.1 Average Value and Area Between Curves Chapter 3 Chapter 4 7.2 Arc Length Chapter 5 Chapter 6 Chapter 7 7.3 Volumes Chapter 8 Chapter 9 7.4 Solids of Revolution Chapter 10 Chapter 11 Chapter 12 7.5 Work Chapter 13 Chapter 14 7.6 Probability Chapter 15 Chapter 16 Revised Sequence
Chapter 8 - Differential Equations Resequencing Calculus: Dwyer and Gruenwald Table of Contents 8.1 Introduction To Differential Equations Chapter 1 Chapter 2 8.2 Symbolic Solutions To Differential Equations Chapter 3 Chapter 4 Chapter 5 8.3 Graphical and Numerical Solutions To Differential Chapter 6 Chapter 7 Equations Chapter 8 Chapter 9 8.4 Exponential Growth and Decay Chapter 10 Chapter 11 Chapter 12 8.5 Logistic Models Chapter 13 Chapter 14 8.6 Linear First Order Differential Equations Chapter 15 Chapter 16 8.7 Difference Equations Revised Sequence
Chapter 9 - Vectors and Matrices Resequencing Calculus: Dwyer and Gruenwald Table of Contents Chapter 1 Chapter 2 9.1 Vectors Chapter 3 Chapter 4 9.2 Dot Product Chapter 5 Chapter 6 Chapter 7 9.3 Matrices Chapter 8 Chapter 9 9.4 Determinants and Inverse Matrices Chapter 10 Chapter 11 Chapter 12 9.5 Cross Product Chapter 13 Chapter 14 9.6 Lines and Planes in Space Chapter 15 Chapter 16 Revised Sequence
Chapter 10 - Functions of Several Variables Resequencing Calculus: Dwyer and Gruenwald Table of Contents 10.1 Introduction to Functions of Several Variables Chapter 1 Chapter 2 10.2 Limits and Continuity Chapter 3 Chapter 4 10.3 Partial Derivatives Chapter 5 Chapter 6 Chapter 7 10.4 Chain Rule Chapter 8 Chapter 9 10.5 Directional Derivatives and Gradients Chapter 10 Chapter 11 Chapter 12 10.6 Tangent Planes and Linear Approximations Chapter 13 Chapter 14 Chapter 15 10.7 Extrema and the Second Partials Test Chapter 16 10.8 Lagrange Multipliers Revised Sequence
Chapter 11 - Double Integrals Resequencing Calculus: Dwyer and Gruenwald Table of Contents Chapter 1 Chapter 2 Chapter 3 Chapter 4 11.1 Double Integrals over Rectangles Chapter 5 Chapter 6 11.2 Double Integrals over Regions Chapter 7 Chapter 8 Chapter 9 11.3 Double Integrals in Polar Coordinates Chapter 10 Chapter 11 11.4 Applications of Double Integrals Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Revised Sequence
Chapter 12 - Infinite Series Resequencing Calculus: Dwyer and Gruenwald 12.1 Sequences of Partial Sums Table of Contents 12.2 Series Chapter 1 Chapter 2 Chapter 3 12.3 Integral Test Chapter 4 Chapter 5 12.4 Comparison Tests Chapter 6 Chapter 7 Chapter 8 12.5 Alternating Series Chapter 9 Chapter 10 12.6 Ratio and Root Tests Chapter 11 Chapter 12 Chapter 13 12.7 Power Series Chapter 14 Chapter 15 12.8 Power Series Representations of Functions Chapter 16 Revised Sequence 12.9 Taylor Series 12.10 Fourier Series
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