Active Calculus

The style of the Active Calculus text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number.

Calculus Mathematics

Tác giả: Matthew Boelkins, David Austin & Steven Schlicker
Nhà xuất bản: Grand Valley State University
Nguồn: LibreTexts
Giấy phép: CC BY-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 96 mục

01: Understanding the Derivative
1.01: How do we Measure Velocity
1.02: The Notion of Limit
1.03: The Derivative of a Function at a Point
1.04: The Derivative Function
1.05: Interpretating Estimating and Using the Derivative
1.06: The Second Derivative
1.07: Limits Continuity and Differentiability
1.08: The Tangent Line Approximation
1.E: Understanding the Derivative (Exercises)
02: Computing Derivatives
2.01: Elementary Derivative Rules
2.02: The Sine and Cosine Function
2.03: The Product and Quotient Rules
2.04: Derivatives of Other Trigonometric Functions
2.05: The Chain Rule
2.06: Derivatives of Inverse Functions
2.07: Derivatives of Functions Given Implicitely
2.08: Using Derivatives to Evaluate Limits
2.E: Computing Derivatives (Exercises)
03: Using Derivatives
3.01: Using Derivatives to Identify Extreme Values
3.02: Using Derivatives to Describe Families of Functions
3.03: Global Optimization
3.04: Applied Optimization
3.05: Related Rates
3.E: Using Derivatives (Exercises)
04: The Definite Integral
4.01: Determining Distance Traveled from Velocity
4.02: Riemann Sums
4.03: The Definite Integral
4.04: The Fundamental Theorem of Calculus
4.E: The Definite Integral (Exercises)
05: Finding Antiderivatives and Evaluating Integrals
5.01: Construction Accurate Graphs of Antiderivatives
5.02: The Second Fundamental Theorem of Calculus
5.03: Integration by Substitution
5.04: Integration by Parts
5.05: Other Options for Finding Algebraic Derivatives
5.06: Numerical Integration
5.E: Finding Antiderivatives and Evaluating Integrals (Exercises)
06: Using Definite Integrals
6.01: Using Definite Integrals to Find Area and Length
6.02: Using Definite Integrals to Find Volume
6.03: Density Mass and Center of Mass
6.04: Physics Applications - Work Force and Pressure
6.05: Improper Integrals
6.E: Using Definite Integrals (Exercises)
07: Differential Equations
7.01: An Introduction to Differential Equations
7.02: Qualitative Behavior of Solutions to Differential Equations
7.03: Euler's Method
7.04: Separable Differential Equations
7.05: Modeling with Differential Equations
7.06: Population Growth and the Logistic Equation
7.E: Differential Equations (Exercises)
08: Sequences and Series
8.01: Sequences
8.02: Geometric Series
8.03: Series of Real Numbers
8.04: Alternating Series
8.05: Taylor Polynomials and Taylor Series
8.06: Power Series
8.E: Sequences and Series (Exercises)
09: Multivariable and Vector Functions
9.01: Functions of Several Variables and Three Dimensional Space
9.02: Vectors
9.03: Dot Product
9.04: The Cross Product
9.05: Lines and Planes in Space
9.06: Vector-Valued Functions
9.07: Derivatives and Integrals of Vector-Valued Functions
9.08: Arc Length and Curvature
10: Derivatives of Multivariable Functions
10.01: Limits
10.02: First-Order Partial Derivatives
10.03: Second-Order Partial Derivatives
10.04: Linearization- Tangent Planes and Differentials
10.05: The Chain Rule
10.06: Directional Derivatives and the Gradient
10.07: Optimization
10.08: Constrained Optimization- Lagrange Multipliers
11: Multiple Integrals
11.01: Double Riemann Sums and Double Integrals over Rectangles
11.02: Iterated Integrals
11.03: Double Integrals over General Regions
11.04: Applications of Double Integrals
11.05: Double Integrals in Polar Coordinates
11.06: Surfaces Defined Parametrically and Surface Area
11.07: Triple Integrals
11.08: Triple Integrals in Cylindrical and Spherical Coordinates
11.09: Change of Variables
12: Appendices
12.01: A- Short Table of Integrals
12.02: B- Answers to Activities
12.03: C- Answers to Selected Exercises