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Maple - The World's First Fully Integrated Analytical Computation System


Student Projects for Introductory Calculus

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 60 projects are available on this site in PDF format.

Integrated Calculus with Analytic Geometry I
Preview individual projects
Download the complete set of basic projects
Download the complete set of honors projects

Integrated Calculus with Analytic Geometry II
Preview individual projects
Download the complete set of basic projects
Download the complete set of honors projects

Integrated Calculus with Analytic Geometry III
Preview individual projects
Download the complete set of basic projects
Download the complete set of honors projects

Basic Projects for Integrated Calculus with Analytic Geometry I
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
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
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
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
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

Honors Projects for Integrated Calculus with Analytic Geometry III
Project 1 Vector Algebra, Lines and Planes
Project 2 Monte Carlo Simulation
Project 3 Curvature of a Curve
Project 4 Motion Around a Circular Path
Project 5 Kepler's Laws of Planetary Motion
Project 6 Optimization for Functions of Three Variables
Project 7 Propagation of Error in Chemistry
Project 8 Visualizing Functions of Several Variables and Animations
Project 9 Painting Arrays with Nested Do-Loops
Project 10 Convolution and Digital Image Processing
Project 11 The Surface Area and Volume of a Manufacturing Tool
Project 12 Limits and Continuity
Project 13 A Strange Function
Project 14 Partial Derivatives
Project 15 Lagrange Multipliers
Project 16 Least Squares
Project 17 Visualizing Regions in R3
Project 18 Transformation from Rectangular to Polar Coordinates
Project 19 Different Strokes...
Project 20 Olber's Black Sky Paradox
Project 21 Iterative Processes and Periodicity Revisited
Project 22 Linear Two-Component Models
Project 23 Interacting Sepecies
Project 24 The Origin of Some Interesting Curves
Project 25 Mechanical Energy of a Coupled Spring-Mass System
Project 26 The Energy of Non-Iteracting Gas Particles
Project 27 The Stretching Potential of a Chemical Bond
Project 28 The Shape of Atomic Orbitals
Project 29 Lissajoux Curves
Project 30 Rotation and Quadric Surfaces