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Math 251 FALL 2004, List of lectures
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Monday, September 27: Mathematical models and functions; four ways
to represent a function. Sections 1.1, 1.2.
Tuesday, September 28: Linear functions, power functions etc.
Inverse functions. Exponential and logarithm. Sections 1.5, 1.6.
Wednesday, September 29: Operations on graphs of functions. The notion
of limit. Sections 1.3, 2.2.
Friday, October 1: Examples when a limit does not exist. One-sided (left
and right) limits. Infinite limits. Section 2.2.
Monday, October 4: Vertical asymptotes. Limit laws. Sections 2.2, 2.3.
Tuesday, October 5: Squeeze Theorem and examples. Section 2.3.
Wednesday, October 6: Continuity and discontinuity. Section 2.5.
Friday, October 8: Continuity and calculation of limits. Intermediate
value theorem. Section 2.5. New homework!
Monday, October 11: Limits at infinity; horizontal asymptotes.
Section 2.6.
Tuesday, October 12: Examples of calculations of limits at infinity;
infinite limites at infinity. Section 2.6. REMINDER: we will have quiz on
Wednesday.
Wednesday, October 13: Reminder on tangent lines. Section 2.7.
We had quiz today;
here are solutions (pdf file).
New homework!
Friday, October 15: Calculation of tangent lines. Velocity. Section 2.7.
Monday, October 18: Velocity and change of rate. Derivative. Sections 2.7,
2.8.
Tuesday, October 19: Derivative: definitions, interpretations, derivative
as a function. Differentiable function is continuous. Sections 2.8, 2.9.
REMINDER: We will have midterm on Friday; review is tomorrow.
Wednesday, October 20: Review before midterm.
New homework!
Friday, October 22: We had midterm today.
Here are the solutions.
Monday, October 25: Derivatives of f(x)=c (constant), f(x)=x, f(x)=x^n;
differentiation rules for multiplication by constant, sum and difference.
Section 3.1.
Tuesday, October 26: Derivative of exponential function; number e;
differentiation rules for the product and ratio. Sections 3.1, 3.2.
Wednesday, October 27: The graph of derivative. Calculation of
derivatives using differentiation rules. Sections 2.9, 3.2.
New homework!
Friday, October 29: Derivatives of trigonometric fucntions;
lim_{h->0}sin(h)/h=1. Section 3.4.
Monday, November 1: Chain rule. Section 3.5.
Tuesday, November 2: Implicit differentiation; derivatives of inverse
trigonometric functions. Section 3.6.
Wednesday, November 3: Derivative of logarithm; logarithmic derivatives;
number e as a limit. Section 3.8. New homework!
We will have QUIZ on Friday, November 5!
Friday, November 5: Different notations for derivatives; higher
derivatives; more on logarithmic derivatives. Sections 3.7, 3.8.
We had quiz today.
Here are the solutions (corrected!
November 8, 2pm).
Monday, November 8: Trigonometric limits; more of implicit
differentiations. Sections 3.4, 3.6. IMPORTANT: We will have another
quiz on Wednesday, November 10 and the midterm on Friday, November 19.
Tuesday, November 9: Related rates. Section 3.10.
Wednesday, November 10: Linear approximations. Section 3.11.
We had quiz today.
Here are the solutions.
New homework!
Friday, November 12: Absolute and relative (=local) maximum (minimum).
Fermat's Theorem. Section 4.1.
Monday, November 15: The closed interval method for absolute maximum
and minimum. Section 4.1.
Tuesday, November 16: When critical point is a local maximum or minimum?
Optimal shape of can. Section 4.7. New homework!
REMINDER: We will have midterm on Friday; review is tomorrow!
Wednesday, November 17: Review before midterm.
Friday, November 19: We had midterm today.
Here are the solutions.
Monday, November 22: The mean value theorem and consequences. Section 4.2.
Tuesday, November 23: Indeterminate forms and L'Hospital's rule.
Section 4.4.
Wednesday, November 24: Further examples of indeterminancies. Section 4.4.
New homework!
Monday, November 29: More of indeterminancies. Section 4.4.
We will have QUIZ on Friday!
Tuesday, Novmber 30: The second derivative test; examples of optimization
problems. Sections 4.3, 4.7.
Wednesday, December 1: Review before final.
Friday, December 3: Review before final.
We had quiz today.
Here are the solutions.
Practice exam is now available.
Solutions are here.