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Calculus 180_Calc I
Contents Calculus I
2.1 The Tangent and Velocity Problems.
2.2 The Limit of a Function.
2.3 Calculating Limits Using the Limit Laws.
2.4 The Precise Definition of a Limit.
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes.
2.7 Derivatives and Rates of Change.
2.8 The Derivative as a Function
3.1 Derivatives of Polynomials and Exponential Functions.
3.2 The Product and Quotient Rules.
3.3 Derivatives of Trigonometric Functions.
3.4 The Chain Rule.
3.5 Implicit Differentiation.
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions.
3.7 Rates of Change in the Natural and Social Sciences.
3.8 Exponential Growth and Decay.
3.9 Related Rates.
3.10 Linear Approximations and Differentials.
3.11 Hyperbolic Functions.
4.1 Maximum and Minimum Values.
4.2 The Mean Value Theorem.
4.3 What Derivatives Tell Us about the Shape of a Graph.
4.4 Indeterminate Forms and l'Hospital's Rule.
4.5 Summary of Curve Sketching.
4.6 Graphing with Calculus and Technology.
4.7 Optimization Problems.
4.8 Newton's Method.
4.9 Antiderivatives.
5.1 The Area and Distance Problems.
5.2 The Definite Integral.
5.3 The Fundamental Theorem of Calculus.
5.4 Indefinite Integrals and the Net Change Theorem.
5.5 The Substitution Rule.
Calculus III
Contents_Calculus III
10.1 Three-Dimensional Coordinate Systems.
10.2 Vectors.
10.3 The Dot Product.
10.4 The Cross Product.
10.5 Equations of Lines and Planes.
10.6 Cylinders and Quadratic Surfaces.
10.7 Vector Functions and Space Curves.
10.8 Arc Length and Curvature.
10.9 Motion in Space: Velocity and Acceleration.
11.1 Functions of Several Variables.
11.2 Limits and Continuity.
11.3 Partial Derivatives.
11.4 Tangent Planes and Linear Approximation.
11.5 The Chain Rule.
11.6 Direction Derivatives and the Gradient Vector.
11.7 Maximum and Minimum Values.
11.8 Lagrange Multipliers.
12.1 Double Integrals over Rectangles.
12.2 Double Integrals over General Regions.
12.3 Double Integrals in Polar Coordinates.
12.4 Applications of Double Integrals.
12.5 Triple Integrals.
12.6 Triple Integrals in Cylindrical Coordinates.
12.7 Triple Integrals in Spherical Coordinates.
12.8 Change of Variables in Multiple Integrals.
13.1 Vector Fields.
13.2 Line Integrals.
13.3 The Fundamental Theorem for Line Integrals.
13.4 Green’s Theorem.
13.5 Curl and Divergence.
13.6 Parametric Surfaces and Their Areas.
13.7 Surface Integrals.
13.8 Stokes’ Theorem.
13.9 The Divergence Theorem.
Home
College Algebra
Contents
1.1 Real Numbers: Algebra Essentials
1.2 Exponents and Scientific Notation.
1.3 Radicals and Rational Exponents.
1.4 Polynomials.
1.5 Factoring Polynomials.
1.6 Rational Expressions.
2.1 Solve Linear Equations in One Variable.
2.2 Solve Linear Equations in Two Variable.
2.3 Slope of a Line.
2.4 Find the Equation of a Line.
2.5 Quadratic Equations.
2.6 Other Types of Equations.
2.7 Linear Inequalities and Absolute Value Inequalities.
3.1 Functions and Function Notation.
3.2 Domain and Range.
3.3 Rates of Change and Behavior of Graphs.
3.4 Composition of Functions
3.5 Inverse Functions
3.6 Transformation of Functions.
3.7 Absolute Value Functions.
4.1 Modeling with Linear Functions.
4.2 System of Linear Functions: Two Variables.
4.3 Solve Applications with Systems of Equations
5.1 Quadratic Functions.
5.2 Power Functions and Polynomial Functions.
5.3 Graphs of Polynomial Functions.
5.4 Rational Functions.
5.5 Modeling Using Variation.
6.1 Graphs of Exponential Functions.
6.2 Exponential Functions.
6.3 Compound Interest and Continuous Exponential Functions.
6.4 Graphs of Logarithmic Functions.
6.5 Logarithmic Functions.
6.6 Logarithmic Properties.
6.7 Exponential and Logarithmic Equations.
6.8 Exponential and Logarithmic Models.
Exams Review
Useful Websites
Math Reasoning for Elementary Teachers
Calculus I Contents and Links to videos
Calculus I Videos
Calculus II
Differential Equations
Contents Differential Equations
1.1 Differential Equations Everywhere.
1.2 Basic Ideas and Terminology.
1.3 The Geometry of First-Order Differential Equations.
1.4 Separable Differential Equations.
1.6 First-Order Linear Differential Equations.
1.7 Modeling Problems Using First-Order Linear Differential Equations.
1.8 Change of Variables.
2.1 Matrices: Definitions and Notation.
2.2 Matrix Algebra.
2.3 Terminology for Systems of Linear Equations.
2.4 Row-Echelon Matrices and Elementary Row Operations.
2.5 Gaussian Elimination.
2.6 The Inverse of a Square Matrix.
3.1 The Definition of the Determinant.
3.2 Properties of Determinants.
3.3 Cofactor Expansions.
4.1 Vectors in R^n .
4.2 Definition of a Vector Space.
4.3 Subspaces.
4.4 Spanning Sets.
4.5 Linear Dependence and Linear Independence.
4.6 Bases and Dimension.
4.8 Row Space and Column Space.
5.1 Definition of an Inner Product Space.
5.2 Orthogonal Sets of Vectors and Orthogonal Projections.
5.3 The Gram-Schmidt Process.
6.1 Definition of a Linear Transformation.
6.3 The Kernel and Range of a Linear Transformation.
6.4 Additional Properties of Linear Transformations.
7.1 The Eigenvalue/Eigenvector Problem.
7.2 General Results for Eigenvalues and Eigenvectors.
7.3 Diagonalization.
7.5 Orthogonal Diagonalization and Quadratic Forms.
8.1 General Theory for Linear Differential Equations.
8.2 Constant Coefficient Homogeneous Linear Differential Equations.
8.3 The Method of Undetermined Coefficients: Annihilators.
8.7 The Variation of Parameters Method.
8.8 A Differential Equation with Nonconstant Coefficients.
9.1 First-Order Linear Systems.
9.2 Vector Formulation.
9.3 General Results for First-Order Linear Differential Systems.
9.4 Vector Differential Equations: Non-defective Coefficient Matrix.
9.5 Vector Differential Equations: Defective Coefficient Matrix.
9.6 Variation-Of-Parameters for Linear Systems.
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Calculus 180_Calc I
Contents Calculus I
2.1 The Tangent and Velocity Problems.
2.2 The Limit of a Function.
2.3 Calculating Limits Using the Limit Laws.
2.4 The Precise Definition of a Limit.
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes.
2.7 Derivatives and Rates of Change.
2.8 The Derivative as a Function
3.1 Derivatives of Polynomials and Exponential Functions.
3.2 The Product and Quotient Rules.
3.3 Derivatives of Trigonometric Functions.
3.4 The Chain Rule.
3.5 Implicit Differentiation.
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions.
3.7 Rates of Change in the Natural and Social Sciences.
3.8 Exponential Growth and Decay.
3.9 Related Rates.
3.10 Linear Approximations and Differentials.
3.11 Hyperbolic Functions.
4.1 Maximum and Minimum Values.
4.2 The Mean Value Theorem.
4.3 What Derivatives Tell Us about the Shape of a Graph.
4.4 Indeterminate Forms and l'Hospital's Rule.
4.5 Summary of Curve Sketching.
4.6 Graphing with Calculus and Technology.
4.7 Optimization Problems.
4.8 Newton's Method.
4.9 Antiderivatives.
5.1 The Area and Distance Problems.
5.2 The Definite Integral.
5.3 The Fundamental Theorem of Calculus.
5.4 Indefinite Integrals and the Net Change Theorem.
5.5 The Substitution Rule.
Calculus III
Contents_Calculus III
10.1 Three-Dimensional Coordinate Systems.
10.2 Vectors.
10.3 The Dot Product.
10.4 The Cross Product.
10.5 Equations of Lines and Planes.
10.6 Cylinders and Quadratic Surfaces.
10.7 Vector Functions and Space Curves.
10.8 Arc Length and Curvature.
10.9 Motion in Space: Velocity and Acceleration.
11.1 Functions of Several Variables.
11.2 Limits and Continuity.
11.3 Partial Derivatives.
11.4 Tangent Planes and Linear Approximation.
11.5 The Chain Rule.
11.6 Direction Derivatives and the Gradient Vector.
11.7 Maximum and Minimum Values.
11.8 Lagrange Multipliers.
12.1 Double Integrals over Rectangles.
12.2 Double Integrals over General Regions.
12.3 Double Integrals in Polar Coordinates.
12.4 Applications of Double Integrals.
12.5 Triple Integrals.
12.6 Triple Integrals in Cylindrical Coordinates.
12.7 Triple Integrals in Spherical Coordinates.
12.8 Change of Variables in Multiple Integrals.
13.1 Vector Fields.
13.2 Line Integrals.
13.3 The Fundamental Theorem for Line Integrals.
13.4 Green’s Theorem.
13.5 Curl and Divergence.
13.6 Parametric Surfaces and Their Areas.
13.7 Surface Integrals.
13.8 Stokes’ Theorem.
13.9 The Divergence Theorem.
Home
College Algebra
Contents
1.1 Real Numbers: Algebra Essentials
1.2 Exponents and Scientific Notation.
1.3 Radicals and Rational Exponents.
1.4 Polynomials.
1.5 Factoring Polynomials.
1.6 Rational Expressions.
2.1 Solve Linear Equations in One Variable.
2.2 Solve Linear Equations in Two Variable.
2.3 Slope of a Line.
2.4 Find the Equation of a Line.
2.5 Quadratic Equations.
2.6 Other Types of Equations.
2.7 Linear Inequalities and Absolute Value Inequalities.
3.1 Functions and Function Notation.
3.2 Domain and Range.
3.3 Rates of Change and Behavior of Graphs.
3.4 Composition of Functions
3.5 Inverse Functions
3.6 Transformation of Functions.
3.7 Absolute Value Functions.
4.1 Modeling with Linear Functions.
4.2 System of Linear Functions: Two Variables.
4.3 Solve Applications with Systems of Equations
5.1 Quadratic Functions.
5.2 Power Functions and Polynomial Functions.
5.3 Graphs of Polynomial Functions.
5.4 Rational Functions.
5.5 Modeling Using Variation.
6.1 Graphs of Exponential Functions.
6.2 Exponential Functions.
6.3 Compound Interest and Continuous Exponential Functions.
6.4 Graphs of Logarithmic Functions.
6.5 Logarithmic Functions.
6.6 Logarithmic Properties.
6.7 Exponential and Logarithmic Equations.
6.8 Exponential and Logarithmic Models.
Exams Review
Useful Websites
Math Reasoning for Elementary Teachers
Calculus I Contents and Links to videos
Calculus I Videos
Calculus II
Differential Equations
Contents Differential Equations
1.1 Differential Equations Everywhere.
1.2 Basic Ideas and Terminology.
1.3 The Geometry of First-Order Differential Equations.
1.4 Separable Differential Equations.
1.6 First-Order Linear Differential Equations.
1.7 Modeling Problems Using First-Order Linear Differential Equations.
1.8 Change of Variables.
2.1 Matrices: Definitions and Notation.
2.2 Matrix Algebra.
2.3 Terminology for Systems of Linear Equations.
2.4 Row-Echelon Matrices and Elementary Row Operations.
2.5 Gaussian Elimination.
2.6 The Inverse of a Square Matrix.
3.1 The Definition of the Determinant.
3.2 Properties of Determinants.
3.3 Cofactor Expansions.
4.1 Vectors in R^n .
4.2 Definition of a Vector Space.
4.3 Subspaces.
4.4 Spanning Sets.
4.5 Linear Dependence and Linear Independence.
4.6 Bases and Dimension.
4.8 Row Space and Column Space.
5.1 Definition of an Inner Product Space.
5.2 Orthogonal Sets of Vectors and Orthogonal Projections.
5.3 The Gram-Schmidt Process.
6.1 Definition of a Linear Transformation.
6.3 The Kernel and Range of a Linear Transformation.
6.4 Additional Properties of Linear Transformations.
7.1 The Eigenvalue/Eigenvector Problem.
7.2 General Results for Eigenvalues and Eigenvectors.
7.3 Diagonalization.
7.5 Orthogonal Diagonalization and Quadratic Forms.
8.1 General Theory for Linear Differential Equations.
8.2 Constant Coefficient Homogeneous Linear Differential Equations.
8.3 The Method of Undetermined Coefficients: Annihilators.
8.7 The Variation of Parameters Method.
8.8 A Differential Equation with Nonconstant Coefficients.
9.1 First-Order Linear Systems.
9.2 Vector Formulation.
9.3 General Results for First-Order Linear Differential Systems.
9.4 Vector Differential Equations: Non-defective Coefficient Matrix.
9.5 Vector Differential Equations: Defective Coefficient Matrix.
9.6 Variation-Of-Parameters for Linear Systems.
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Folder:
Calculus 180_Calc I
Folder:
Calculus III
Home
Folder:
College Algebra
Useful Websites
Math Reasoning for Elementary Teachers
Calculus I Contents and Links to videos
Calculus I Videos
Calculus II
Folder:
Differential Equations
Back
Contents Calculus I
2.1 The Tangent and Velocity Problems.
2.2 The Limit of a Function.
2.3 Calculating Limits Using the Limit Laws.
2.4 The Precise Definition of a Limit.
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes.
2.7 Derivatives and Rates of Change.
2.8 The Derivative as a Function
3.1 Derivatives of Polynomials and Exponential Functions.
3.2 The Product and Quotient Rules.
3.3 Derivatives of Trigonometric Functions.
3.4 The Chain Rule.
3.5 Implicit Differentiation.
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions.
3.7 Rates of Change in the Natural and Social Sciences.
3.8 Exponential Growth and Decay.
3.9 Related Rates.
3.10 Linear Approximations and Differentials.
3.11 Hyperbolic Functions.
4.1 Maximum and Minimum Values.
4.2 The Mean Value Theorem.
4.3 What Derivatives Tell Us about the Shape of a Graph.
4.4 Indeterminate Forms and l'Hospital's Rule.
4.5 Summary of Curve Sketching.
4.6 Graphing with Calculus and Technology.
4.7 Optimization Problems.
4.8 Newton's Method.
4.9 Antiderivatives.
5.1 The Area and Distance Problems.
5.2 The Definite Integral.
5.3 The Fundamental Theorem of Calculus.
5.4 Indefinite Integrals and the Net Change Theorem.
5.5 The Substitution Rule.
Back
Contents_Calculus III
10.1 Three-Dimensional Coordinate Systems.
10.2 Vectors.
10.3 The Dot Product.
10.4 The Cross Product.
10.5 Equations of Lines and Planes.
10.6 Cylinders and Quadratic Surfaces.
10.7 Vector Functions and Space Curves.
10.8 Arc Length and Curvature.
10.9 Motion in Space: Velocity and Acceleration.
11.1 Functions of Several Variables.
11.2 Limits and Continuity.
11.3 Partial Derivatives.
11.4 Tangent Planes and Linear Approximation.
11.5 The Chain Rule.
11.6 Direction Derivatives and the Gradient Vector.
11.7 Maximum and Minimum Values.
11.8 Lagrange Multipliers.
12.1 Double Integrals over Rectangles.
12.2 Double Integrals over General Regions.
12.3 Double Integrals in Polar Coordinates.
12.4 Applications of Double Integrals.
12.5 Triple Integrals.
12.6 Triple Integrals in Cylindrical Coordinates.
12.7 Triple Integrals in Spherical Coordinates.
12.8 Change of Variables in Multiple Integrals.
13.1 Vector Fields.
13.2 Line Integrals.
13.3 The Fundamental Theorem for Line Integrals.
13.4 Green’s Theorem.
13.5 Curl and Divergence.
13.6 Parametric Surfaces and Their Areas.
13.7 Surface Integrals.
13.8 Stokes’ Theorem.
13.9 The Divergence Theorem.
Back
Contents
1.1 Real Numbers: Algebra Essentials
1.2 Exponents and Scientific Notation.
1.3 Radicals and Rational Exponents.
1.4 Polynomials.
1.5 Factoring Polynomials.
1.6 Rational Expressions.
2.1 Solve Linear Equations in One Variable.
2.2 Solve Linear Equations in Two Variable.
2.3 Slope of a Line.
2.4 Find the Equation of a Line.
2.5 Quadratic Equations.
2.6 Other Types of Equations.
2.7 Linear Inequalities and Absolute Value Inequalities.
3.1 Functions and Function Notation.
3.2 Domain and Range.
3.3 Rates of Change and Behavior of Graphs.
3.4 Composition of Functions
3.5 Inverse Functions
3.6 Transformation of Functions.
3.7 Absolute Value Functions.
4.1 Modeling with Linear Functions.
4.2 System of Linear Functions: Two Variables.
4.3 Solve Applications with Systems of Equations
5.1 Quadratic Functions.
5.2 Power Functions and Polynomial Functions.
5.3 Graphs of Polynomial Functions.
5.4 Rational Functions.
5.5 Modeling Using Variation.
6.1 Graphs of Exponential Functions.
6.2 Exponential Functions.
6.3 Compound Interest and Continuous Exponential Functions.
6.4 Graphs of Logarithmic Functions.
6.5 Logarithmic Functions.
6.6 Logarithmic Properties.
6.7 Exponential and Logarithmic Equations.
6.8 Exponential and Logarithmic Models.
Exams Review
Back
Contents Differential Equations
1.1 Differential Equations Everywhere.
1.2 Basic Ideas and Terminology.
1.3 The Geometry of First-Order Differential Equations.
1.4 Separable Differential Equations.
1.6 First-Order Linear Differential Equations.
1.7 Modeling Problems Using First-Order Linear Differential Equations.
1.8 Change of Variables.
2.1 Matrices: Definitions and Notation.
2.2 Matrix Algebra.
2.3 Terminology for Systems of Linear Equations.
2.4 Row-Echelon Matrices and Elementary Row Operations.
2.5 Gaussian Elimination.
2.6 The Inverse of a Square Matrix.
3.1 The Definition of the Determinant.
3.2 Properties of Determinants.
3.3 Cofactor Expansions.
4.1 Vectors in R^n .
4.2 Definition of a Vector Space.
4.3 Subspaces.
4.4 Spanning Sets.
4.5 Linear Dependence and Linear Independence.
4.6 Bases and Dimension.
4.8 Row Space and Column Space.
5.1 Definition of an Inner Product Space.
5.2 Orthogonal Sets of Vectors and Orthogonal Projections.
5.3 The Gram-Schmidt Process.
6.1 Definition of a Linear Transformation.
6.3 The Kernel and Range of a Linear Transformation.
6.4 Additional Properties of Linear Transformations.
7.1 The Eigenvalue/Eigenvector Problem.
7.2 General Results for Eigenvalues and Eigenvectors.
7.3 Diagonalization.
7.5 Orthogonal Diagonalization and Quadratic Forms.
8.1 General Theory for Linear Differential Equations.
8.2 Constant Coefficient Homogeneous Linear Differential Equations.
8.3 The Method of Undetermined Coefficients: Annihilators.
8.7 The Variation of Parameters Method.
8.8 A Differential Equation with Nonconstant Coefficients.
9.1 First-Order Linear Systems.
9.2 Vector Formulation.
9.3 General Results for First-Order Linear Differential Systems.
9.4 Vector Differential Equations: Non-defective Coefficient Matrix.
9.5 Vector Differential Equations: Defective Coefficient Matrix.
9.6 Variation-Of-Parameters for Linear Systems.
Chapter One:
First-Order Differential Equations.
1.1 Differential Equations Everywhere.
