Math 251 FALL 2004, List of lectures

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.