Calculus by David Guichard (Improved)

This is an improved version of LibreTexts edition of Calculus by David Guidhard which has been edited by Terry Betteridge. Many interactive figures have been added as well as correcting misprints.

Calculus Mathematics

Tác giả: Terry Betteridge, Editor
Nhà xuất bản: LibreTexts
Nguồn: LibreTexts
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 132 mục

01: Analytic Geometry
1.01: Prelude to Analytic Geometry
1.02: Lines
1.03: Distance Between Two Points Circles
1.04: Functions
1.05: Shifts and Dilations
02: Instantaneous Rate of Change- The Derivative
2.01: The Slope of a Function
2.02: An Example
2.03: Limits
2.04: The Derivative Function
2.05: Adjectives for Functions
03: Rules for Finding Derivatives
3.01: The Power Rule
3.02: Linearity of the Derivative
3.03: The Product Rule
3.04: The Quotient Rule
3.05: The Chain Rule
04: Transcendental Functions
4.01: Trigonometric Functions
4.02: The Derivative of sin x
4.03: A Hard Limit
4.04: The Derivative of sin x - II
4.05: Derivatives of the Trigonometric Functions
4.06: Exponential and Logarithmic Functions
4.07: Derivatives of the Exponential and Logarithmic Functions
4.08: Implicit Differentiation
4.09: Inverse Trigonometric Functions
4.10: Limits Revisited
4.11: Hyperbolic Functions
05: Curve Sketching
5.01: Maxima and Minima
5.02: The First Derivative Test
5.03: The Second Derivative Test
5.04: Concavity and Inflection Points
5.05: Asymptotes and Other Things to Look For
06: Applications of the Derivative
6.01: Optimization
6.02: Related Rates
6.03: Newton's Method
6.04: Linear Approximations
6.05: The Mean Value Theorem
07: Integration
7.01: Two Examples
7.02: The Fundamental Theorem of Calculus
7.03: Some Properties of Integrals
08: Techniques of Integration
8.01: Substitution
8.02: Powers of sine and cosine
8.03: Trigonometric Substitutions
8.04: Integration by Parts
8.05: Rational Functions
8.06: Numerical Integration
8.07: Additional exercises
09: Applications of Integration
9.01: Area Between Curves
9.02: Distance Velocity and Acceleration
9.03: Volume
9.04: Average Value of a Function
9.05: Work
9.06: Center of Mass
9.07: Kinetic energy and Improper Integrals
9.08: Probability
9.09: Arc Length
9.10: Surface Area
10: Polar Coordinates and Parametric Equations
10.01: Polar Coordinates
10.02: Slopes in Polar Coordinates
10.03: Areas in Polar Coordinates
10.04: Parametric Equations
10.05: Calculus with Parametric Equations
11: Sequences and Series
11.01: Prelude to Sequences and Series
11.02: Sequences
11.03: Series
11.04: The Integral Test
11.05: Alternating Series
11.06: Comparison Test
11.07: Absolute Convergence
11.08: The Ratio and Root Tests
11.09: Power Series
11.10: Calculus with Power Series
11.11: Taylor Series
11.12: Taylor's Theorem
11.13: Additional Exercises
12: Three Dimensions
12.01: The Coordinate System
12.02: Vectors
12.03: The Dot Product
12.04: The Cross Product
12.05: Lines and Planes
12.06: Other Coordinate Systems
13: Vector Functions
13.01: Space Curves
13.02: Calculus with Vector Functions
13.03: Arc length and Curvature
13.04: Motion Along a Curve
14: Partial Differentiation
14.01: Functions of Several Variables
14.02: Limits and Continuity
14.03: Partial Differentiation
14.04: The Chain Rule
14.05: Directional Derivatives
14.06: Higher order Derivatives
14.07: Maxima and minima
14.08: Lagrange Multipliers
15: Multiple Integration
15.01: Volume and Average Height
15.02: Double Integrals in Cylindrical Coordinates
15.03: Moment and Center of Mass
15.04: Surface Area
15.05: Triple Integrals
15.06: Cylindrical and Spherical Coordinates
15.07: Change of Variables
16: Vector Calculus
16.01: Vector Fields
16.02: Line Integrals
16.03: The Fundamental Theorem of Line Integrals
16.04: Green's Theorem
16.05: Divergence and Curl
16.06: Vector Functions for Surfaces
16.07: Surface Integrals
16.08: Stokes's Theorem
16.09: The Divergence Theorem
17: Differential Equations
17.01: First Order Differential Equations
17.02: First Order Homogeneous Linear Equations
17.03: First Order Linear Equations
17.04: Approximation
17.05: Second Order Homogeneous Equations
17.06: Second Order Linear Equations
17.07: Second Order Linear Equations II