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640:135 - Calculus I

Lecture Topics

1 1.2, 1.3 Precalculus Review: Real line, coordinate plane, distance, circles, straight lines.
2 1.4 Precalculus Review: Functions, graphs. Trig review: Radians, definition of trig functions, graphs of sin, cos, tan, sec.
3 2.1, 2.2 Limits: Definition and discussion of intuitive meaning. Rules for limits, computing limits of algebraic functions. One sided limits, squeeze theorem, limits for trig functions, infinite limits.
4 2.2 Topics of lecture 3, continued.
5 2.3 Continuity, intermediate value theorem, finding roots.
6 2.4 Exponentials and logarithms: Definition of e, properties and inverse relation of exp and ln. Compound interest, future value, exponential population growth.
7 3.1 Definition of the derivative: Direct calculation of derivatives. Relation between the graph of f and the graph of f'. Continuity and differentiability.
8 3.2, 3.3 Calculation: Sum, product and quotient rules. Higher order derivatives. Differentiation of exponential and trig functions.
9 3.4 The derivative as a rate of change. Velocity and acceleration.
10 3.5 Chain rule.
11   Catch up and review.
13 3.6 Implicit differentiation. Derivatives of log and exp to other bases. Derivative of log(|u|). Logarithmic differentiaion
14 3.7 Related rates.
15 3.8 Linear approximation. Differentials. Error and relative error of measurement. Marginal analysis.
16 4.1, 4.2 Optimization of a continuous function on a bounded interval. Statement of mean value theorem and examples 1 & 2.
17 4.3 First and second derivative analysis and curve sketching.
18 4.4 Curve sketching with asymptotes. Limits as x approaches plus or minus infinity.
19 4.5 L'Hopitals's rule.
20 4.6 Optimization applications: Physical problems.
21   Catch up and review.
23 4.7 Optimization applications: Marginal analysis and profit maximization, inventory problems, physiology problems.
24 5.1 Antiderivatives.
25 5.2, 5.3 Riemann sums and the definition of definite integrals.
26 5.4 Fundamental theorems of calculus.
27 5.5 Substitution method for both indefinite and definite integrals.
28   Catch up and review.

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