CATALOG DESCRIPTION: |
|
Primarily for students in the engineering technologies. Topics include exponential, logarithmic and trigonometric functions; analytic geometry; limits; and derivatives, integrals and their applications.
|
LEARNING OBJECTIVES: |
Upon completion of this course, the student will be able to:
- Use the definitions and basic terminology of logarithms, derivatives and integral.
- Use the basic terminology of slope, conic sections and polar coordinates.
- Perform differentiation, integration and numerical integration.
- Graph conic sections and systems of equations.
- Solve trigonometric identities and equations.
- Solve applied derivative problems.
|
COURSE OUTLINE: |
Logarithms:
- Definition and Graphs
- Properties of Logarithms
- Common and Natural Logarithms
- Exponential and Logarithmic Equations
- Graphs on Log Paper
Plane Analytical Geometry:
- Definition of Slope
- Equations of The Straight Line
- Basic Definitions and The Conic Sections
- The General Second Degree Equation
- Polar Coordinates and Curves
- Polar Curves
Solutions of Other Equations:
- Graphical Solutions of Systems of Equations
- Algebraic Solutions of Systems of Equations
- Equations in Quadratic Form
- Radical Equations
Additional Topics in Trigonometry:
- Fundamental Identities
- Sum and Difference Identities
- Double angle Identities
- Trigonometric Equations
- Inverse Trigonometric Functions
The Derivative:
- Limits
- Definition of Derivative and Its Interpretation
- Finding Derivatives
- Higher Derivatives (omit implicit higher derivatives)
Applications of The Derivative:
- Tangents and Normals
- Parametric Curves and Curvilinear Motion
- Related Rates
- Curve Sketching
- Maximum and Minimum Problems
Integration:
- Antidevrivatives
- Indefinite Integrals
- Areas under curves and definite integrals
- Trapezoidal Rule and Simpson's Rule
Differentiation of Transcendental Functions:
- Differentiation of Trigonometric Functions
- Applications of Trigonometric Derivatives (excluding derivatives of inverse trigonometric functions)
- Differentiation of Logarithmic and Exponential Functions
- Applications
|
