11.1 Functions of Several Variables. — Lecture videos with pictures and simplified examples.

Skip to Content

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.

2.6 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.

Contents_Calculus III

10.1 Three-Dimensional Coordinate Systems.

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.

College Algebra

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.

Useful Websites

Math Reasoning for Elementary Teachers

Calculus I Contents and Links to videos

Calculus I Videos

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.

2.6 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.

Contents_Calculus III

10.1 Three-Dimensional Coordinate Systems.

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.

College Algebra

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.

Useful Websites

Math Reasoning for Elementary Teachers

Calculus I Contents and Links to videos

Calculus I Videos

Folder: 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.

2.6 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.

Folder: Calculus III

Contents_Calculus III

10.1 Three-Dimensional Coordinate Systems.

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.

Folder: College Algebra

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.

Useful Websites

Math Reasoning for Elementary Teachers

Calculus I Contents and Links to videos

Calculus I Videos

Chapter 11: Partial Derivatives.

11.1 Functions of Several Variables.

Functions of Several Variables.