- Combined Calculus
- Chapter 0
- 01) Examples 1 and 2
- 02) Example 3
- 03) Example 5
- 04) Example 6
- 05) Example 9
- 06) Example 10
- 07) Example 11
- 08) Example 12
- 09) Example 13
- 10) Example 14
- 11) Example 15
- 12) Calculator
- 01) Lesson
- 02) Example 1
- 03) Example 2
- 04) Example 5
- 05) Example 6
- 01) Example 2
- 02) Example 5
- 03) Example 6
- 04) Example 7
- 05) Completing the Square
- 01) Example 1
- 02) Example 2
- 03) Example 3
- 04) Example 4
- 05) Example 5
- 06) Example 7
- 07) Example 8
- 08) Example 9
- 09) Quadratic Formula
- 01) Example 1
- 02) Example 2
- 03) Example 3
- 04) Example 4
- 05) Example 5
- 06) Example 6
- 07) Solving Inequalities
- 08) Solving Inequalities 2
Chapter 0.1: Solving Linear Equations
Chapter 0.2: Solving Equations of the form ax^2 - b =0
Chapter 0.3: Completing the Square
Chapter 0.4: The Quadratic Formula and Applications
Chapter 0.5: Solving Non-Linear Inequalities
- Appendix
- 01) Matrices: Application from Business
- 02) Matrices: Application from Business 2
- 03) Matrices: 3-Variable Example
- 04) Basic Operations and Definitions
- 05) Dimension
- 06) Matrix Addition and Scalar Multiplication
- 07) Practice on Scalar Multiplication, Zero Matrix
- 08) Problems Similar to Homework
- 09) Problems Similar to Homework 2
- 10) Problem from Homework
- 01) Introduction
- 02) Vector Multiplication-2 Examples
- 03) Vector Mult: (Cont’d)
- 04) Vector Mult: Practice
- 05) Matrix Mult: (1x3)(3x2)
- 06) Matrix Mult: (3x3)(3x2) and General Notation
- 07) Matrix Mult: (2x3)(3x2)
- 08) Matrix Mult: AB vs. BA
- 09) Matrix Mult: Practice w/ Dimensions
- 10) Matrix Mult: (2,3) entry
- 11) Matrix Mult: Discovering I
- 12) Matrix Mult: Inverses
- 13) Matrix Mult: Showing Inverse
- 14) Properties of Matrices
- 15) Matrices, Systems of Equations, and AX=B
- 16) Solving 2x2 System using AX=B
- 17) Summary of Previous Solution
- 18) Solve 3x3 System Using AX=B
- 19) Definition AT (Transpose)
- 20) Practice AT
- 21) Calculator: Vector Multiplication
- 22) Calculator: Matrix Multiplication
- 01) Introductory Problem
- 02) Intro.to Augmented Matrix
- 03) A General Augmented Matrix
- 04) Elimination Needed for Gauss-Jordan Row Reduction
- 05) Checking Solution from Video 4
- 06) Gauss-Jordan Row Reduction [G-JRR] on Example from Video 4
- 07) 2-Variable Example of G-JRR
- 08) 3-Variable Example of G-JRR
- 09) 3-Variable Example of G-JRR
- 10) Using G-JRR to find A-1
- 11) Finding 3x3 Inverse
- 12) Finding Another 3x3 Inverse
- 13) Summary of 2.3
- 14) What’s to Come in 2.4
- 15) Row Operations on the TI-89
- 16) G-JRR on Calculator
- 17) Using GJ-RR to find A-1 on TI-89
- 18) Discussion About Memory
- 01) Introduction to Inconsistent System
- 02) RREF Form and Inconsistent Systems
- 03) 2x2 System w/ Infinitely Many Solutions
- 04) Types of Solutions to Systems of Linear Equations in 2 Variables
- 05) Possible Types of Solutions in 3 Variables
- 06) Types of Solutions in 3 Variables (Cont’d)
- 07) Alternative Theorem and Proof
- 08) Inconsistent Systems-3 Variables
- 09) Infinitely Many Solutions-2 Variables
- 10) Infinitely Many Solutions-3 Variables
- 11) Example from Book-4 Variables
- 12) Example from Book-4 Variables
- 13) Calculator Tip-RREF
- 14) “Word Problem” using Calculator
- 15) Verifying RREF and Writing Solution
- 16) Verifying RREF and Writing Solution (Cont’d)
- 17) Verifying RREF and Writing Solution (Cont’d)
- 18) Another Example with 4x5 Matrix
- 19) Another 4x5 Matrix
- 20) Final 4x5 Matrix
- 21) Summary of Chapter 2
A.1: Basic Operations
A.2: Matrix Multiplication
A.3: Gauss-Jordan Row Reduction
A.4: Inconsistent Linear Systems and Systems with Infinitely Many Solutions
- Chapter 1
- 01) Example 1
- 02) Example 1, pt.2
- 03) Example 2
- 04) Example 3
- 05) Example 4
- 06) Example 6
- 07) Perpendicular Lines
- 01) Example 1
- 02) Example 4
- 03) Example 5
- 04) Example 7
- 05) Example 10
- 06) Example 11
- 07) Example 12
- 08) Example 13
- 09) Example 14
- 10) Example 16
- 11) Rationalize Denominator
- 12) Calculator Tips
- 13) Calculator Tips 2
- 01) Example 1
- 02) Example 2
- 03) Example 3
- 04) Linear Functions
- 05) Depreciation
- 01) Quadratic Functions
- 02) Figure 5
- 03) Horizontal Translation
- 04) Example 1
- 05) Completing square - standard form
- 06) General procedure - standard form
- 07) Example 3
- 08) Example 5
- 09) Example 6
- 10) Example 7
- 11) Calculator Tips
- 01) The Circle
- 02) Example 1
- 03) Example 2
- 04) Examples 3,4 and 5
- 05) Example 6
- 06) Tangent Line 1
- 07) Tangent Line 2
- 08) Tangent Line 3
- 09) Ellipse, Figure 6
- 10) Ellipse, standard form
- 11) Calculator Tips
- 01) Example 1
- 02) Example 2
- 03) Example 3
- 04) Example 4
- 05) Example 5
- 06) Example 7
- 07) Marginal Function
- 08) Demand Function
- 09) Revenue
- 10) Calculator Tips
- 01) Example 1
- 02) Example 2
- 03) Example 3
- 04) Example 4
- 05) Example 5
- 06) Example 6
- 07) Example 7
- 08) Example 8
- 09) Example 9
- 10) Exampe 10
- 11) Symmetry
- 12) Using Zeros
- 13) Translations
- 01) Data Points
- 02) Example 1
- 03) Example 2
- 04) Calculator Tips
Chapter 1.1: The Line
Chapter 1.2: Basic Notions of Functions
Chapter 1.3: Applications of Linear Functions
Chapter 1.4: Quadratic Functions
Chapter 1.5: The Circle
Chapter 1.6: Economic Functions
Chapter 1.7: More on Functions
Chapter 1.8: Regression
- Chapter 2
- 01) Introduction
- 02) Intro. (Cont’d) and Average Rate of Change
- 03) Average Rate of Change (Cont’d)
- 04) Ave. and Instantaneous Rate of Change
- 05) Approximating Instantaneous Rate of Change, Part I
- 06) Approximating Instantaneous Rate of Change, Part II
- 07) Approximating Instantaneous Rate of Change, Part III
- 08) Introduction to Slope of Curve/Tangent Line
- 09) Slope of Secant Approximating Slope of Tangent
- 10) The Slope as a Limit
- 11) Finding Slope of Tangent to a Curve at a Point
- 12) Finding Slope to Curve (Cont’d)
- 13) Finding Slope of Tangent, Example 2
- 14) Finding Slope of Curve at 4 Different Points
- 15) Slope at 4 Different Points (Cont’d)
- 16) Intro to Using Calculator
- 17) Calculator Tips-Slope of Tangent Line
- 18) Equation of Tangent Line Part I
- 19) Equation of Tangent Line, Part II
- 20) Equation of Tangent Line, Part III
- 21) Equation of Tangent Line, Part IV
- 22) Introduction to Slope of Square Root Functions
- 23) Finding Slopes of Square Root Functions, Part I
- 24) Calculator Investigation of Square Root Problem
- 25) Finding Slopes of Square Root Functions, Part II
- 26) Finding Equation of Tangent Line to Square Root Function
- 27) Slope of Square Root Function, Example 2
- 28) Slope of Square Root Function at Any x
- 29) Existence of Tangent Line, Part I
- 30) Existence of Tangent Line, Part II
- 31) Existence of Tangent Line, Part III
- 32) Slope of a Piecewise-Defined Function
- 33) The Derivative and its Notation, Part I
- 34) Derivative Notation, Part II
- 35) Derivative of Cubic Function, Part I
- 36) Derivative of Cubic Function, Part II
- 37) Calculator Tip for Homework Problems
- 01) Introduction-Derivative of xn
- 02) Derivatives of Linear and Constant Functions of Derivative of xn, Part I
- 03) Proof of Derivative of xn, Part II
- 04) Review of Laws of Exponents, Part I
- 05) Review of Laws of Exponents, Part II
- 06) Constant Multiplier Rule and Examples
- 07) The Sum Rule and Examples
- 08) Derivative of a Polynomial
- 09) Equation of Tangent Line
- 10) Equation Tangent Line and Error
- 11) Understanding Percent Error
- 12) Calculators Tips
- 01) Intro. to Limits, Part I
- 02) Intro. to Limits, Part II
- 03) Intro. to Limits, Part III
- 04) Intro. to Limits, Part IV
- 05) Intro. to Limits, Part V
- 06) Intro. to Limits, Part VI
- 07) Limit Example 1
- 08) Limit Example 2
- 09) Limit Example 3
- 10) Limit Practice Problem
- 11) Theorem 1: Limit of Constant
- 12) Thm 2: Limit of x
- 13) Thm 3: Limit of kf(x)
- 14) Thm 4: Limit of f(x) + g(x)
- 15) Thm 5: Limit of f(x)g(x)
- 16) Thm 6: Limit of f(x)/g(x)
- 17) Thm 7: Limit of [f(x)]^N
- 18) Limit of Square Root
- 19) Limits Using Theorems
- 20) Limit of Difference Quotient
- 21) Another Difference Quotient Limit
- 22) One-Sided Limits
- 23) Limits of Piecewise Defined Functions
- 24) Piecewise Defined with "Hole"
- 25) Piecewise Defined with "Jump"
- 26) Piecewise Limit without Graph
- 27) Practice with Piecewise
- 28) Continuity, Part I
- 29) Continuity, Part II
- 30) Continuity, Part III
- 31) Definition of Continuous
- 32) Example: "Discuss Continuity"
- 33) Differentiability and Continuity
- 01) Why Division by 0 is Undefined and 0/0 Indeterminate
- 02) Lim as x->0+ of 1/x
- 03) Lim as x->0- of 1/x
- 04) Lim as x->0 of 1/x
- 05) Lim as x->0 of 1/x2
- 06) Lim as x->0 of -1/x2 and Shortcut to Finding Infinite Limits
- 07) Lim as x->2 of 1/(x-2)
- 08) 4 Examples of Infinite Limits
- 09) Lim as x->a+ of 1/(x-a)n
- 10) Lim as x->a- of 1/(x-a)n and lim x->-3- of x/(x+3)
- 11) Lim as x->-3+ of x/(x+3)
- 12) Lim as x->-7-
- 13) 2 More Infinite Limits
- 14) Pond Problem 1
- 15) Pond Problem 2
- 16) Pond Problem 3
- 17) Lim as x->infinity of (100,000 + 215x) / x
- 18) Shortcuts for 2 Limits at Infinity
- 19) 3 Limits x-> Infinity
- 20) More Limits at Infinity, and Summary
- 21) Sketch Graph of Rational Function
- 22) TI-89: Finding Limits
- 23) TI-89: Finding Limits at Infinity and Infinite Limits Exactly
- 24) A Problem Similar to Homework, Part I
- 25) A Problem from Homework, Part II
- 26) Another Homework Problem
- 01) Summary of Derivative Rules
- 02) Motivating Product Rule
- 03) Product Rule Example 1
- 04) Product Rule Example 2
- 05) Product Rule Example 3
- 06) Product Rule with Square Root
- 07) Motivating Quotient Rule
- 08) Another Quotient to Differentiate
- 09) Quotient Rule Example 1
- 10) Quotient Rule Example 2
- 11) Quotient Rule Example 3
- 12) Using TI-89 to Show Equivalent Expressions
- 01) Review/Derivative of Composite Function
- 02) Motivating the Chain Rule
- 03) Chain Rule
- 04) Chain Rule Example
- 05) Chain Rule Example 2
- 06) Chain Rule Example 3
- 07) General Power Rule
- 08) Equation of Tangent Line
- 09) Derivative of Square Root with Chain Rule
- 10) Product and Chain Rules Together
- 11) Chain, then Quotient Rule
- 12) Quotient, then Chain Rule
- 13) Another Use for Chain Rule, Part I
- 14) Another Use for Chain Rule, Part II
- 01) Marginal Cost, Example 1
- 02) Marginal Cost, Example 2
- 03) Practice Finding Marginal Cost
- 04) Definition of Marginals
- 05) Intro to Derivative
- 06) Summary of Marginal vs. Derivative
- 07) E'(x) approximates E(x+1) - E(x)
- 08) Practice: Change in Revenue
- 09) Percent Error of Approximation
- 10) Average Cost, Revenue, or Profit
- 11) TI-89 and Average Rate of Change
- 12) Vertical Motion, Part I
- 13) Vertical Motion, Part II
- 14) Vertical Motion, Part III
- 15) Average vs. Instantaneous Velocity
- 16) Why Derivative Gives Instant. ROC
- 17) Problems Using ROC, Part I
- 18) Problems Using ROC, Part II
- 19) Practice with Instant. Vel.
- 01) Intro. to Implicit Differentiation
- 02) Slope of a Circle, Part I
- 03) Slope of a Circle using Imp. Diff.
- 04) Equation of Tangent to Circle
- 05) Practice: Equation Tangent Line
- 06) Imp. Diff. Example 4
- 07) Imp. Diff. Example 5
- 08) Imp. Diff. Example 6
- 09) Imp. Diff. Example 7
- 10) Imp. Diff. Example 8
- 11) TI-89 and Implicit Differentiation
- 01) Related Rates: Shuttle Launch
- 02) Shuttle Launch, Part II
- 03) Oil Spill
- 04) Shadows and Similar Triangles
- 01) Newton's Method
- 02) Newton's Method on Excel
- 03) Newton's Method on TI-89
Chapter 2.1: Slope of a Curve
Chapter 2.2: Derivative Rules I
Chapter 2.3: Limits and Continuity
Chapter 2.4: Limits at Infinity, Infinite Limits and Asymptotes
Chapter 2.5: Derivative Rules 2
Chapter 2.6: The Chain Rule
Chapter 2.7: Marginal Funcations and Rates of Change
Chapter 2.8: Implicit Differentiation
Chapter 2.10: Related Rates
Chapter 2.11: Newton's Method
- Chapter 3
- 01) Continuous Functions and Intervals
- 02) Maximums and Minimums
- 03) Extreme Value Theorem
- 04) Relative Max. and Min.
- 05) Critical Numbers and Points
- 06) Example 2 and 3
- 07) Finding Extreme Values
- 08) Critical Point Test Theroem
- 09) Example 6
- 01) First Derivative test
- 02) Examples 1 and 2
- 03) Example 3
- 04) Example 4
- 05) Example 5
- 06) Example 6
- 01) Higher Order Derivatives
- 02) Example 2
- 03) Example 3
- 04) Example 4
- 05) Concavity and Points of Inflection
- 06) Concavity and 2nd Derivative
- 07) Example 5
- 08) 2nd Derivative Test for Relative Extrema
- 09) Example 6
- 10) Example 8
- 11) Example 10
- 12) Example 11
- 13) Example 12
- 14) Implicit Differentiation
- 01) Examples 1 and 2
- 02) Example 3: Rancher
- 03) Example 4: Open Top
- 04) Example 5: River
- 01) Example 1
- 02) Example 2: Bicycles
- 03) Example 3: Average Cost
- 04) Example 4: Stereos
- 05) Example 5: Theatre
- 06) Elasticity of Demand
- 07) Elasticity of Demand Revisited
- 08) Relative Change
- 01) Linearization
- 02) Example 1
- 03) Examples 2 and 3
- 04) Differentials
- 05) Example not in textbook
- 06) Example 5: Bacteria
- 07) Relative Change
- 08) Analysis of E
- 09) Differential Formulas
Chapter 3.1: Extrema of a Function
Chapter 3.2: First Derivative Test
Chapter 3.3: Concavity and the Second Derivative
Chapter 3.4: Geometric Optimization Problems
Chapter 3.5: Business and Economic Optimization Problems
Chapter 3.6: Linearization and Differentials
- Chapter 4
- 01) intro
- 02) Example 1
- 03) Composition Property
- 04) Example 2
- 05) Practice 1
- 06) Practice 2
- 07) One to One Example
- 08) One to One Definition
- 09) One to One Practice
- 10) Practice with Inverses
- 11) Derivative of Inverse Function
- 12) Practice of Inverse Prime
- 13) Calculator Example
- 01) A New Function
- 02) Exploring Exponential Functions
- 03) Practice
- 04) Practice 2
- 05) Solving Special Exponential Equations
- 06) Exponential Functions from Data
- 07) Exponential Turtle Example
- 08) Growth Decay Formulas
- 09) Calculator Example
- 10) Calculator Example 2
- 01) Matching the Graphs of Exp Functions
- 02) Compound Interest
- 03) Discovering e
- 04) Practice Compound Continuously
- 05) Graph of e to x
- 07) Excel Example
- 08) Excel Example 2
- 01) Investigating Derivative of e to x
- 02) Example 1
- 03) Example 2
- 04) Example 3
- 05) Example 4
- 06) Implicit Differentiation
- 07) Extrema and Concave Graphs
- 08) Calculator Example
- 09) Calculator Example 2
- 01) Introduction to Logs
- 02) Decay Example: Solve for t, Part 1
- 03) Decay Example: Solve for t, Part 2
- 04) Inverse y equals 2 to x
- 05) Inverse y equals 10 to x
- 06) Practice evaluating logs
- 07) Calc. Practice: Napiers Bones
- 08) Logorithms ph
- 09) Graphs and transformation
- 10) y equals in x minus 1
- 11) y equlas in plus minus e
- 12) Derivative of f of x
- 13) Generalized Logorithmic
- 14) Calculator Example
- 15) Calculator Example 2
- 16) Calculator Example 3
- 01) Properties of Logs
- 02) Multiplication Property of Logs
- 03) Division Property of Logs
- 04) Practice with Properties
- 05) Discovering Exponential Property
- 06) Using the Property
- 07) Derivatives Using Properties
- 08) Solving Logarithmic Equations
- 09) Solving Exponential Equations
- 10) t in Compound Interest Problems
- 11) Solving for r and t
- 12) Change of Base
- 13) Derivative and Change of Base
- 14) Logarithmic Differentiation
- 15) Calculator Example
- 01) Introduction
- 02) Investment Example
- 03) Bacterial Growth Example
- 04) Radioactive Decay
- 05) Carbon Dating
- 06) Logistical Growth and Richtor Scale
- 07) Sea Lion Hint
- 08) Calculator Example
Chapter 4.1: Inverse Functions
Chapter 4.2: Exponential Functions
Chapter 4.3: The Number e
Chapter 4.4: The Derivative of e
Chapter 4.5: Logarithmic Functions
Chapter 4.6: Properties of Logarithmic Functions
Chapter 4.7: Applications of Exponential and Logarithmic Functions
- Chapter 5
- 01) Antidifferentiation
- 02) More Differentiation Practice
- 03) Using the Sum/Difference Rule
- 04) Results with ln "x" and e
- 05) Calculator Example
- 06) Families of Antiderivatives
- 01) Graphs and Particular Solutions
- 02) Solving Differential Equations
- 03) Motion Equations: Part 1
- 04) Motion Equations: Part 2
- 05) Marginal Cost and Revenue
- 06) Separable Differential Equations
- 07) Calculator Example
- 01) The Substitution Method
- 02) Examples
- 03) Technique of Substitution
- 04) Generalized Rules
- 05) Practice Using Substitution
- 06) More Practice wtih Substitution
- 07) Calculator Example
- 01) Approximation of Areas
- 02) Endpoints
- 03) Practice with Endpoints and Midpoints
- 04) Excel Example
- 01) Sigma Notation and Area
- 02) Practice with Summation
- 03) Area Under a Curve
- 04) Example 1
- 05) Example 2
- 06) Calculator Example
- 01) The Definite Integral and Fundamental Theorem
- 02) Practice 1
- 03) Practice 2
- 04) Properties of the Definite Integral
- 05) Area Problem
- 06) Calculator Example
- 01) Substitution and Properties of the Definite Integra
- 02) Even and Odd Functions
- 03) Average Value
- 04) Derivative of Definite Integral
- 05) Calculator Example
- 06) Calculator Example 2
- 01) Introduction
- 02) Example 1
- 03) Example 2
- 04) Example 3
- 05) Consumer Surplus
- 06) Producer Surplus
- 07) Continuous Income Flow
- 08) Probability Density Functions
- 09) Calculator Example
- 10) Calculator Example 2
- 11) Calculator Example 3
- 12) Calculator Example 4
Chapter 5.1: Antidifferentiation - Integration
Chapter 5.2: Applications of Antidifferentiation
Chapter 5.3: The Substitution Method
Chapter 5.4: Approximation of Areas
Chapter 5.5: Sigma Notation and Areas
Chapter 5.6: The Definite Integral
Chapter 5.7: Substitution and Properties of the Definite Integral
Chapter 5.8: Applications of the Definite Integral
- Chapter 6
- 01) Example 1 - Function of 2 Variables
- 02) Example 2 - Function of 3 Variables
- 03) Difference Quotients
- 04) Three Dimensional Coordinates
- 05) Calculator Example
- 06) Calculator Example 2
- 01) Notation and Example 1
- 02) Examples 2 and 3
- 03) Visualization and Example 4
- 04) Examples 5 and 6
- 05) Level Curves / Contours
- 06) Example 7
- 07) Cobb Douglas Production Function
- 08) Example 8
- 09) Example 9
- 10) Level Indifference Curve
- 11) Utility Function Example
- 12) Higher Order Example 1
- 13) Higher Order Example 2
- 14) Calculator Example
- 01) Definitions
- 02) Saddle Points and Example 1
- 03) Example 2
- 04) Example 3
- 05) Example 4
- 06) Second Partial Derivatives
- 07) Example 5
- 08) Example 6
- 09) Example 7
- 10) Open Rectangular Box Example
- 11) Calculator Example
- 01) Lagrange Multipliers: Example 1
- 02) Example 2
- 03) Example 3
- 04) Example 4
- 05) Calculator Example
- 01) Product Example 1
- 02) Product Example 2
- 03) Product Example 3
- 04) Cobb Douglas Production Example
- 05) The Marginal Rate of Substitution
- 06) Utility Function Example
Chapter 6.1: Functions of Several Variables
Chapter 6.2: Partial Derivatives
Chapter 6.3: Extrema
Chapter 6.4: The Method of Lagrange Multipliers
Chapter 6.5: Economic Applications
Chapter 4.2: Exponential Functions - 05) Solving Special Exponential Equations
One Bernard Baruch Way (55 Lexington Ave. at 24th St)
New York, NY 10010 646-312-1000
