Department of Mathematics

Syllabus

**Inter 01.315 PATTERNS IN NATURE II: CALCULUS AND PHYSICS**

**Catalog Description**

**Inter 01.315** **Patterns in Nature II: CALCULUS AND PHYSICS ****
4 s.h.**

Prerequisites: Math 01.315 Patterns in Nature I

This course actively involves students in developing mathematics and
science concepts associated with calculus and physics while de-emphasizing
algorithms. Problems arise from physics and are analyzed using mathematical
models. Graphing calculators, computers, and physical models are used extensively.

**OBJECTIVES:**

Students completing this course will be able to:

- use functions to model a variety of problem situations, investigating
the properties of these functions through appropriate technologies, including
graphing calculators;

- use physical models, charts, graphs, equations, and inequalities to describe real-world relationships;

- use graphs, diagrams, and physical models to interpret and relate the concepts of limit, differentiation, and integration;

- apply quantitative techniques to the analysis of problems involving
motion and spectra.

- Functions as models; parameterization
- Rates of change; motion
- Gradients of curves and first principles
- Polynomial approximations
- Optimization
- Velocity as a vector
- Changes in motion
- Force
- Numerical integration
- Algebraic integration
- Volume & arc length
- Projectiles as motion under a force
- Projectiles and Force
- Force as vectors
- Circular motion
- Rigid bodies
- Work and energy
- Scalar products
- Potential energy
- Modeling circular motion
- Simple Harmonic Motion
- Waves
- Photons & photoelectric effect
- Quantum Mechanics
- Spectroscopy

**TEXTS**:

Five books from Cambridge University 16-19 Mathematics series

*NEWTON'S LAWS OF MOTION*

*MODELING WITH CIRCULAR MOTION*

*MODELING WITH FORCE AND MOTION*

*INTRODUCTORY CALCULUS*

*CALCULUS METHODS*