## Operation Mother Hen

Operation Mother Hen is a partnership between the Department of Mathematics and Science and Engineering Node Services (SENS). With support from a Faculty Educational Technology Grant from the University at Buffalo, Operation Mother Hen began as a pilot project in the fall of 1999.

The purpose of Operation Mother Hen is to provide entry-level calculus students with an opportunity to review the material that was presented in class by viewing video clips of their instructor as she demonstrates the basic principles of calculus. Operation Mother Hen is not intended as a substitute for class attendance, but rather as a supplement to class attendance. With Operation Mother Hen, students may review the basics as many times as they need to from any internet-connected computer.

## System Requirements

Operation Mother Hen requires that you have a computer with an internet connection (the faster the better, of course!) and an audio output device if you wish to have sound for the video lectures.

Mobile devices are supported.

## Course Content

#### MTH141 - College Calculus I

Excerpts from Professor Ann Piech's MTH 141 lectures. The excerpts cover basic calculus concepts with examples. Chapters 2 through 5 of Calculus, by Edwards & Penney.

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##### Chapter 2 - Limits and Derivatives
 2.1 The Tangent and Velocity Problems Section 2.1 Notes Tangent Line Slope of the Tangent Line Example Instantaneous Velocity Slope Velocity Connection Slope Formula 2.2 Volumes Section 2.2 Notes Informal Definition of the Limit Limit Pictures More Limit Pictures Vertical Asymptotes, Infinite Limits Example Calculating Infinite Limits Example You Try It 2.3 Calculating Limits Using the Limit Laws Section 2.3 Notes Limit Laws Useful Limit Facts Limit Examples Limit Examples Continued The Squeeze Law Squeeze Law Example 2.4 The Precise Definition of a Limit Section 2.4 Notes Limit Practice Precise Definition of a Limit Example Example - A Limit Proof 2.5 Continuity Section 2.5 Notes Definitions of Continuity Picture Examples of Continuity & Discontinuity Continuity on an Interval Building Continous Functions Examples of Continous Functions Intermediate Value Theorem Example Using Intermediate Value Theorem 2.6 Limits at Infinity; Horizontal Asymptotes Section 2.6 Notes Horizontal Asymptotes Examples of Horizontal Asymptotes More Examples Limits of Infinity More Examples Limits of Infinity 2 2.7 Tangents, Velocities, and Other Rates of Change Section 2.7 Notes Slope Formula Slope Velocity Derivative Example 1 Calculating m from Limit Definition Example 2 Calculating from Limit Definition Another Form For m 2.8 Derivatives Section 2.8 Notes The Derivative Example: Derivative Calculation 2.9 The Derivative as a Function Section 2.9 Notes The Derivative as a Function Differentiability Implies Continuity Pictures Relating Graphs of f and f'
##### Chapter 3 - Differentiation Rules
 3.1 Derivatives of Polynomials and Exponential Functions Section 3.1 Notes Basic Differentation Rules 1 Basic Differentation Rules 2 Examples of Derivative of Polynomial Derivative of Exponential Function Examples - Differentation 3.2 The Product and Quotient Rules Section 3.2 Notes Product Rule, Quotient Rule Examples Differentation 1 Examples Differentation 2 Examples Differentation 3 3.3 Rates of Change Section 3.3 Notes Delta Y Delta X Notation Straight Line Motion Example of Straight Line Motion Derivative Interpretations 1 Derivative Interpretations 2 3.4 Derivatives of Trigonometric Functions Section 3.4 Notes Important Trig Limit Examples of Trig Limits The Derivatives of Sine x Derivative Interpretations 1 Trig Derivative Formulas Examples of Trig Differentation 3.5 The Chain Rule Section 3.5 Notes The Chain Rule Motivation for Chain Rule Using the Chain Rule Example Chain Rule 1 Example Chain Rule 2 Example Chain Rule 3 3.6 Implicit Differentiation Section 3.6 Notes Impilicit Differentation Example Implicit Differentation 1 Example Implicit Differentation 2 Derivative of the Inverse Sine Inverse Trig Derivative Formulas Examples of Inverse Trig Differentiation 3.7 Higher Derivatives Section 3.7 Notes Higher Derivatives Examples Higher Derivatives Second Derivative by Implicit Differentation 3.8 Derivatives of Logarithmic Functions Section 3.8 Notes The Derivative Derivative of ln x Differentiation Examples Logarithmic Differentiation Example 1 - Logarithmic Differentiation Example 2 - Logarithmic Differentiation 3.11 Linear Approximation and Differentials Section 3.11 Notes The Linear Approximation Differential Notation Example Estimating Maximum Error
##### Chapter 4 - Applications of Differentiation
 4.1 Maximum and Minimum Values Section 4.1 Notes Absolute Maximum & Minimum Pictures Local Maximum & Minimum Pictures Extreme Value Theorem Calculus Steps for Finding Absolute Extrema Example 1 Max Min Values Example 2 Max Min Values 4.2 Mean Value Theorem Section 4.2 Notes Mean Value Theorem & Rolle's Theorem Pictures of Rolle's MV Theorems Consequences of the Mean Value Theorem Example Finding c for MV Theorem Example Exactly One Real Root Example Growth of f 4.3 How Derivatives Affect the Shape of a Graph Section 4.3 Notes What does f' say About the Graph f Example First Derivative Analysis What does f'' say About the Graph of f Example Second Derivative Analysis Example Graphing with Derivative Analysis 4.4 Indeterminate Forms and L'Hospital's Rule Section 4.4 Notes L'Hospital's Rule Using L'Hospital's Rule L'H Example Indeterminate Forms Another L'H Example (1) Another L'H Example (2) 4.5 Summary of Curve Sketching Section 4.5 Notes Curve Sketching with Calculus Techniques Slant Asymptotes Checklist for Curve Sketching Graphing Example 1 Graphing Example 1 Concluded Graphing Example 2 Graphing Example 2 Concluded 4.6 This section omitted 4.7 Optimization Problems Section 4.7 Notes Tests for Absolute Max/Min Example 1 Example 1 continued Example 1 Concluded Example 2 Minimizing Distance Example 2 Concluded 4.8 This section omitted 4.9 Newton's Method Section 4.9 Notes About Newton's Method Newton's Method Formula for xn + 1 Example Newton's Method Comments on Newton's Method 4.10 Antiderivatives Section 4.10 Notes Antiderivatives Examples of General Antiderivatives F(x) More Antiderivative Examples More Examples 1 More Examples 2 Vertical Motion Example Vertical Motion
##### Chapter 5 - Integrals
 5.1 Areas and Distances Section 5.1 Notes Area Under a Graph Area Under a Graph 2 Example Estimating Distance Traveled Distance and Area Example Estimating Area 5.2 Definite Integral Section 5.2 Notes Riemann Sums & Definite Integral Interpretation of Definite Integral as Signed Area Examples Evaluation Integrals in Terms of Area Properites of the Definite Integral 1 Properties of the Definite Integral 2 Midpoint Rule for Evaluating a Definite Integral 5.3 The Fundamental Theorem of Calculus Section 5.3 Notes The Fundamental Theorem of Calculus Fundamental Theorem Continued Examples Differentating Integrals Example Evaluating Definite Integrals 5.4 Indefinite Integrals and the Total Change Theorem Section 5.4 Notes Indefinite Integrals Integral Formulas Total Change Displacement & Distance Traveled Example 5.5 The Substitution Rule Section 5.5 Notes Example 1 Substitution in Indefinite Integrals Example 2 Substitution in Indefinite Integrals Useful Comments on Substitution Examples 3 & 4 Substitution in Indefinite Integrals Example 1 Substitution in Defiinite Integrals Example 2 Substitution in Definite Integrals Example 3 Substitution in Definite Integrals

#### MTH142 - College Calculus II

Excerpts from Professor Ann Piech's MTH 142 lectures. The excerpts cover basic calculus concepts with examples. Chapters 6 through 11 of Single Variable Calculus, UB Edition (or Calculus, Early Transcendentals, 4th Edition), by James Stewart.

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##### Chapter 6
 6.1 Areas Between Curves Section 6.1 Notes Area Between Two Curves Setting Up Area Integrals 2 Area Example 1 Area Example 2 Area Example 6.2 Volumes Section 6.2 Notes Volumes by Cross-Sections Volume of Solid of Revolution by Disks Example 1 Volume by Disks Volume of Solid of Revolution by Washers Example 2 Volume by Washers 6.3 Volumes by Cylindrical Shells Section 6.3 Notes Section 6.2/6.3 FAQ Volumes of Cylindrical Shells Volumes of Cylindrical Shells 2 Volume of Cylindrical Shells 3 Example 1 Cylindrical Shells Example 2 Cylindrical Shells 6.5 Average Value of a Function Section 6.5 Notes Average Value of f(x) Mean Value Theorem for Integrals Average Value Example
##### Chapter 7
 7.1 Integration by Parts Section 7.1 Notes Integration by Parts Example 1 Integration by Parts Example 2 Integration by Parts Example 3 Integration by Parts Example Definite Integral by Parts Example 2 Definite Integral by Parts 7.2 Trigonometric Integrals Section 7.2 Notes Integrals of Sines and Cosines 1 Integrals of Sines and Cosines 2 Integrals of Sines and Cosines 3 Integrals with Tan, Sec, etc 1 Integrals with Tan, Sec, etc 2 Integrals with Tan Sec, etc 3 7.3 Trigonometric Substitutions Section 7.3 Notes Trig Substitutions Example 1 Sine Substitution Example 2 Secant Substitution Example 3 Tangent Substitution 7.4 Integration of Rational Functions by Partial Fractions Section 7.4 Notes Section 7.4 FAQ Integrating Rational Functions 1 Integrating Rational Functions 2 Partial Fraction Expansions 1 Partial Fraction Expansions 2 Partial Fractions Example 1 Partial Fractions Example 2 Partial Fractions Example 3 7.7 Approximate Integration Section 7.7 Notes Approximate (Numerical) Integration The Midpoint Rule The Trapezodial Rule Example Trapedozial Rule Simpson's Rule Example Simpson's Rule Comparison of Rules 7.8 Improper Integrals Section 7.8 Notes Improper Integrals 1 Improper Integrals 2 Improper Integrals 3 Setting Up Improper Integrals 1 Setting Up Improper Integrals 2 Example Improper Integrals 1 Example Improper Integrals 2
##### Chapter 8
 8.1 Arc Length Section 8.1 Notes Length of a Smooth Curve Arc Length Formulas Example Arc Length 1 Example Arc Length 2 8.2 Area of a Surface of Revolution Section 8.2 Notes Area of Surface of Revolution Example Surface Area Comments
##### Chapter 9
 9.4 Exponential Growth and Decay Section 9.4 Notes Natural (Exponential) Growth Solution of Natural Growth Differential Equation Example Bacteria Growth Example Radioactive Decay Example Radioactive Decay Concluded
##### Chapter 10
 10.1 Curves Defined by Parametric Equations Section 10.1 Notes Parametric Curves Parametric Circles Eliminating Parameters Importance of Parametric Curves 10.2 Tangents and Areas Section 10.2 Notes Derivaties of Parametric Curves Example Finding Derivatives Example Curve Sketching Example Curve Sketching Conclusion Area Under a Parametric Curve 10.3 Arc Length and Surface Area Section 10.3 Notes Arc Length for a Parametric Curve Example Arc Length Surface Area of Revolution Example Surface Area 10.4 Polar Coordinates Section 10.4 Notes Definition of Polar Coordinates Conversion Between Polar and Cartesian Coordinates Example 1 Sketching Polar Curves Example 2 Sketching Polar Curves Example 2 Sketching Polar Curves Concluded Example 3 Sketching Polar Curves Tangents to Polar Curves 10.5 Areas and Lengths in Polar Coordinates Section 10.5 Notes dA in Polar Coordinates Example 1 Area Inside Cardiod Area Between 2 Polar Curves Example Area Between Curves Pt 1 Example Area Between Curves Pt 2 Length of Polar Curves
##### Chapter 11
 11.1 Sequences Section 11.1 Notes Sequences Finding Sequence Limits Sequence Examples 1 Sequence Examples 2 11.2 Series Section 11.2 Notes Infinite Series Connection with Improper Integrals Basic Questions About Series Geometric Series 1 Geometric Series 2 Example Geometric Series Example Repeating Decimals 11.3 The Integral Test and Estimates of Sums Section 11.3 Notes The Integral Test Example 1 Integral Test Example 2 Integral Test Example 3 P-Series Estimating the Sum of a Series 11.4 The Comparison Tests Section 11.4 Notes Comparison Tests Series to Compare With Examples Limit Comparison 1 Examples Limit Comparison 2 Examples Ordinary Comparison 11.5 Alternating Series Section 11.5 Notes Alternating Series Convergence Picture and Remainder Estimate Examples Alternating Series Examples Alternating Series 2 Examples Remainder (Error) Estimate 11.6 Absolute Convergence and the Ratio and Root Tests Section 11.6 Notes Absolute and Conditional Convergence 1 Absolute and Conditional Convergence 2 The Ratio Test and the Root Test Examples Ratio and Root Tests 1 Examples Ratio and Root Tests 2 Examples Ratio and Root Tests 3 Examples Ratio and Root Tests 4 11.8 Power Series Section 11.8 Notes Power Series Interval of Convergence Examples Power Series 1 Examples Power Series 2 Examples Power Series 2 Concluded Examples Power Series 3 Examples Power Series 4 11.9 Representations of Functions as Power Series Section 11.9 Notes Power Series Representations Example 1 Differentiation or Integration of Power Series Example Evaluating Integrals Using Power Series 11.10 Taylor and Maclaurin Series Section 11.10 Notes 1-3 Taylor & Maclaurin Series Taylor Polynomial & Remainder Estimate Example Maclaurin Series for e^x Section 11.10 Notes 4-9 Example Maclaurin Series for cos x Example - A Taylor Series Maclaurin Series to Know Example More Maclaurin Series Example Series Approximation of Definite Integral Example Series Approximation of Definite Integral Concluded 11.11 The Binomial Series Section 11.11 Notes The Binomial Series Example 1 Example 2 Example 3 11.12 Applications of Taylor Polynomials Section 11.12 Notes Taylor Polynomials Approximation by Taylor Polynomials Example 1 Example 1 Continued Example 1 Concluded