Calculus

Mathematics

Tác giả: Eric Hutchinson
Nhà xuất bản: College of Southern Nevada
Nguồn: LibreTexts
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 129 mục

01: Functions and Graphs (Precalculus Review)
1.01: Review of Functions
1.02: Basic Classes of Functions
1.03: Trigonometric Functions
1.04: Inverse Functions
1.05: Exponential and Logarithmic Functions
02: Limits and Continuity
2.01: Limit of a Function and Limit Laws
2.02: The Precise Definition of a Limit
2.03: One-Sided Limits
2.04: Continuity
2.05: Limits Involving Infinity Asymptotes of Graphs
03: Differentiation
3.01: Defining the Derivative
3.02: The Derivative as a Function
3.03: Differentiation Rules
3.04: The Derivative as a Rate of Change
3.05: Derivatives of Trigonometric Functions
3.06: The Chain Rule
3.07: Implicit Differentiation
3.08: Derivatives of Inverse and Logarithmic Functions
3.09: Inverse Trigonometric Functions
3.10: Related Rates
3.11: Linearization and Differentials
04: Applications of Derivatives
4.01: Maxima and Minima
4.02: The Mean Value Theorem
4.03: The First Derivative Test
4.04: The Second Derivative Test and Curve Sketching
4.05: Indeterminate Forms and L'Hopital's Rule
4.06: Applied Optimization Problems
4.07: Newton's Method
05: Integration
5.01: Antiderivatives
5.02: Approximating Areas with Limits of Finite Sums
5.03: The Definite Integral
5.04: The Fundamental Theorem of Calculus
5.05: Substitution with Indefinite Integrals
5.06: Substitution with Definite Integrals
06: Applications of Definite Integrals
6.01: Volumes Using Cross-Sections
6.02: Volumes Using Cylindrical Shells
6.03: Arc Length
6.04: Areas of Surfaces of Revolution
6.05: Work
6.06: Moments and Centers of Mass
07: Integrals and Transcendental Functions
7.01: The Logarithm Defined as an Integral
7.02: Exponential Change and Separable Differential Equations
7.03: Hyperbolic Functions
08: Techniques of Integration
8.01: Integration by Parts
8.02: Trigonometric Integrals
8.03: Trigonometric Substitutions
8.04: Integration of Rational Functions by Partial Fractions
8.05: Integral Tables and Computer Algebra Systems
8.06: Numerical Integration
8.07: Improper Integrals
09: Infinite Sequence and Series
9.01: The Binomial Series and Applications of Taylor Series
9.02: Sequences
9.03: Infinite Series
9.04: The Integral Test
9.05: Comparison Tests
9.06: The Ratio and Root Tests
9.07: Alternating Series Absolute and Conditional Convergence
9.08: Power Series
9.09: Taylor and Maclaurin Series
9.10: Convergence of Taylor Series
10: Parametric Equations and Polar Coordinates
10.01: Parametrizations of Plane Curves
10.02: Calculus with Parametric Curves
10.03: Polar Coordinates
10.04: Graphing in Polar Coordinates
10.05: Areas and Lengths in Polar Coordinates
10.06: Conics in Polar Coordinates
11: Vectors and the Geometry of Space
11.01: Three-Dimensional Coordinate Systems
11.02: Vectors
11.03: The Dot Product
11.04: The Cross Product
11.05: Lines and Planes in Space
11.06: Cylinders and Quadric Surfaces
12: Vector-Valued Functions and Motion in Space
12.01: Curves in Space and Their Tangents
12.02: Integrals of Vector Functions Projectile Motion
12.03: Arc Length in Space
12.04: Curvature and Normal Vectors of a Curve
12.05: Tangential and Normal Components of Acceleration
12.06: Velocity and Acceleration in Polar Coordinates
13: Partial Derivatives
13.01: Functions of Several Variables
13.02: Limits and Continuity in Higher Dimensions
13.03: Partial Derivatives
13.04: The Chain Rule
13.05: Directional Derivatives and Gradient Vectors
13.06: Tangent Planes and Differentials
13.07: Extreme Values and Saddle Points
13.08: Lagrange Multipliers
14: Multiple Integrals
14.01: Double and Iterated Integrals over Rectangles
14.02: Double Integrals over General Regions
14.03: Area by Double Integration
14.04: Double Integrals in Polar Form
14.05: Triple Integrals in Rectangular Coordinates
14.06: Moments and Centers of Mass
14.07: Triple Integrals in Cylindrical and Spherical Coordinates
14.08: Substitutions in Multiple Integrals
15: Integration in Vector Fields
15.01: Line Integrals
15.02: Vector Fields and Line Integrals- Work Circulation and Flux
15.03: Path Independence Conservative Fields and Potential Functions
15.04: Green's Theorem in the Plane
15.05: Surfaces and Area
15.06: Surface Integrals
15.07: Stokes' Theorem
15.08: The Divergence Theorem and a Unified Theory
16: First-Order Differential Equations
16.01: Solutions Slope Fields and Euler's Method
16.02: First-Order Linear Equations
16.03: Applications
16.04: Graphical Solutions of Autonomous Equations
16.05: Systems of Equations and Phase Planes
17: Second-Order Differential Equations
17.01: Second-Order Linear Equations
17.02: Nonhomogeneous Linear Equations
17.03: Applications
17.04: Euler Equations
17.05: Power Series Solutions