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
2.2 Volumes
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 Tangents, Velocities, and Other Rates of Change
2.8 Derivatives
2.9 The Derivative as a Function
Chapter 3 - Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Rates of Change
3.4 Derivatives of Trigonometric Functions
3.5 The Chain Rule
3.6 Implicit Differentiation
3.7 Higher Derivatives
3.8 Derivatives of Logarithmic Functions
3.11 Linear Approximation and Differentials
Chapter 4 - Applications of Differentiation
4.1 Maximum and Minimum Values
4.2 Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Indeterminate Forms and L'Hospital's Rule
4.5 Summary of Curve Sketching
4.6 This section omitted
4.7 Optimization Problems
4.8 This section omitted
4.9 Newton's Method
4.10 Antiderivatives
Chapter 5 - Integrals
5.1 Areas and Distances
5.2 Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Total Change Theorem
5.5 The Substitution Rule

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
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.5 Average Value of a Function
Chapter 7
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitutions
7.4 Integration of Rational Functions by Partial Fractions
7.7 Approximate Integration
7.8 Improper Integrals
Chapter 8
8.1 Arc Length
8.2 Area of a Surface of Revolution
Chapter 9
9.4 Exponential Growth and Decay
Chapter 10
10.1 Curves Defined by Parametric Equations
10.2 Tangents and Areas
10.3 Arc Length and Surface Area
10.4 Polar Coordinates
10.5 Areas and Lengths in Polar Coordinates
Chapter 11
11.1 Sequences
11.2 Series
11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series
11.6 Absolute Convergence and the Ratio and Root Tests
11.8 Power Series
11.9 Representations of Functions as Power Series
11.10 Taylor and Maclaurin Series
11.11 The Binomial Series
11.12 Applications of Taylor Polynomials