Student Projects for Introductory Calculus
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Student Projects for Introductory Calculus
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These student projects have been developed by the mathematics department of IUPUI for their introductory calculus sequence Integrated Calculus with Analytic Geometry I and II. Each project begins with a brief review of a topic that has been presented in lecture. The student is then guided through a Maple exploration of the topic. Projects are rated as either Basic or Honors. Basic projects are mandatory for all students in the course. Honors projects are offered as extra credit or used for honors sections. All 100 projects are available on this site in PDF format.
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Basic Projects for Integrated Calculus with Analytic Geometry I |
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| Project 1 | Arithmetic and Simple Algebra using Maple |
| Project 2 | Functions of a Single Variable and Graphing |
| Project 3 | Guessing Limits Numerically |
| Project 4 | The Precise Definition of a Limit |
| Project 5 | Ballistics |
| Project 6 | Differentiation |
| Project 7 | Linear Approximation and Differentials |
| Project 8 | The Mean Value Theorem |
| Project 9 | Concavity and Inflection Points |
| Project 10 | Graphing Functions |
| Project 11 | Newton's Method |
| Project 12 | Integration: Riemann Sums |
| Project 13 | The Fundamental Theorem of Calculus |
| Project 14 | Surfaces of Revolution |
Honors Projects for Integrated Calculus with Analytic Geometry I |
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| Project 1 | The Iteration Method for Finding Roots |
| Project 2 | Iteration and Chaos |
| Project 3 | Variations in the Graph of a Function |
| Project 4 | Variations in the Graph of the Sine Function |
| Project 5 | Function Addition |
| Project 6 | Tangential Approximation |
| Project 7 | Graphing a Function Using a Table |
| Project 8 | Implicit Functions and Implicit Differentiation |
| Project 9 | Maximum and Minimum Values on a Closed Interval |
| Project 10 | Graphing Functions Again |
| Project 10 | Graphing Functions One More Time |
| Project 10 | The Fundamental Theorem of Calculus |
| Project 11 | The Average Value of a Function |
Basic Projects for Integrated Calculus with Analytic Geometry II |
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| Project 1 | Inverse Functions |
| Project 2 | Exponential Functions |
| Project 3 | Logarithmic Identities and Inequalities |
| Project 4 | Techniques of Integration |
| Project 5 | Approximate Integration |
| Project 6 | Newton's Law of Cooling |
| Project 7 | Direction Fields |
| Project 8 | The Logistic Equation |
| Project 9 | Parametrized Curves |
| Project 10 | Ballistics with Parametric Curves |
| Project 11 | Polar Curves in Cartesian Coordinates |
| Project 12 | Sequences and Series |
| Project 13 | More Sequences and Series |
| Project 14 | Maclaurin Series |
Honors Projects for Integrated Calculus with Analytic Geometry II |
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| Project 1 | Exponential Growth and Decay |
| Project 2 | Exponentials, Logarithms and Their Derivatives |
| Project 3 | Power Functions |
| Project 4 | Partial Fractions |
| Project 5 | Drug Dosage |
| Project 6 | Least Squares |
| Project 7 | Tracer Methods in Permeability |
| Project 8 | Improper Integrals and Black Holes |
| Project 9 | Spring-Mass Damping |
| Project 10 | Coupled Spring-Mass Systems |
| Project 11 | Finite Differences |
| Project 12 | Euler's Method |
| Project 13 | Another Population Model, Stability and Equilibria |
| Project 14 | An Epidemic |
| Project 15 | Differential vs. Difference Equations |
| Project 16 | Ballistics with Air Resistence |
| Project 17 | Escape Velocity |
| Project 18 | Bezier Curves |
| Project 19 | More Bezier Curves |
| Project 20 | Rectangular vs. Polar Coordinates |
| Project 21 | Limacons |
| Project 22 | The Order of Functions |
| Project 23 | Vibration in Molecules |
Basic Projects for Integrated Calculus with Analytic Geometry III |
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| Project 1 | 3_D Graphics, Lines and Planes |
| Project 2 | Cylinders and Quadric Surfaces |
| Project 3 | Rectangular, Cylindrical and Spherical Coordinates |
| Project 4 | Curves in Space |
| Project 5 | Graphs of Functions |
| Project 6 | Function Optimization |
| Project 7 | Constrained Optimization |
| Project 8 | Double Integrals |
| Project 9 | Transformations of the Plane |
| Project 10 | Vector Fields in the Plane |
| Project 11 | Line Integrals in the Plane |
| Project 12 | Drawing Surfaces |
| Project 13 | Surface Area and Surface Integrals |
