This support course will cover a SUBSET of these topics in just-in-time remediation for success in the Math 160 Calculus and Analytical Geometry I course:
Develop study habits that promote success in Math 160, such as the use of test preparation and metacognitive strategies to improve understanding and performance.
2. Functions and graphing
Graphs of rational functions, exponential functions, log functions
Graphs of all six trigonometric functions including period changes, amplitude changes, and shifts
Graphs of arcsine, arccosine, arctangent functions
Graphs of polar functions
Graphs of parametrically defined curves
Calculator usage with respect to graphs
3. Trigonometry
a. Review of unit circle
b.. Trig Inverse values
c. Right triangle trigonometry,
d. compositions of trig and trig inverses, creating algebraic expressions involving x
e .Trigonometric identities (Statements and proofs)
4. Algebra
Laws of logarithms and exponents
Simplifying with factorials
Polynomial Long-division
Partial Fractioning
5. Geometry
Writing algebraic expressions for areas and volumes of common geometric shapes
Writing algebraic expressions using similar triangles and right triangle trigonometry
Circumference of a circle, area of a sector of a circle
6. Sequences and Series
Sequence and summation notation, including developing a formula for a sequence or series/pattern recognition, standard conventions.
Arithmetic and geometric sequences and series, including modeling a word problems with a series
7. Logic and Proof
Review of if-then statements, if-and-only-if statements.
Converse, inverse, and contrapositive.
Induction.
8 Vectors
2d-vector representations (componentwise, direction/magnitude, between two points)
Vector plotting
Vector algebra
Applications of vectors (simple work problems assuming a constant force)
9. Calculus I
Limits, in particular limits at infinity, including techniques such as squeeze theorem and L’Hospital’s Rule as well a graphically and algebraically.
Physical Interpretation of derivative: slope of the tangent line and instantaneous rate of change.
Differentiation rules and techniques
Mean Value Theorem (derivative form)
Simple differential equations and initial value problems (such as f ''=2x+sin(x), f(0)=2, f '(0)=1)
Common antiderivatives and guess and check integrating
Integral techniques: substitution and integration by parts
Definition of definite Integral (as limit of a Riemann Sum) and area interpretation
Midpoint Rule for approximating a definite integral
The Fundamental Theorem of Calculus (both parts)