Math 149 - Calculus I
Class Journal
Textbook: Calculus by Larson, Hostetler, Edwards, Eighth Edition
| Date | Topics covered |
| Mon. Aug 31 | A simple function and what it could represent; linear equations, their graphs, slope, and intercept |
| Wed. Sep 2 | (Class met in the lab). Basics of DERIVE, Fitting models to data |
| Fri. Sep 4 | Quiz 1, Horizontal, vertical, perpendicular, parallel lines, functions, domain, range, and graph of a function, sign chart, intersection of two curves |
| Mon. Sep 7 | Finding intersection of curves, intercepts of graphs, implicit, explicit functions, equation of a circle, evaluating a function, composition of functions, Investigating the behavior of a function at a given point (Example: f(x) = sin (x-5)/(x-5) at x=5). |
| Wed. Sep 9 | limits, left limit, right limit, examples |
| Fri. Sep 11 | Quiz 2, piecewise-defined functions, their limits, computations with infinity |
| Mon. Sep 14 | when does a limit exist, finding limits analytically, examples |
| Wed. Sep 16 | infinite limits |
| Fri. Sep 18 | Exam 1 |
| Mon. Sep 21 | Continuity, absolute value function, greatest integer function and their graphs |
| Wed. Sep 23 | More on the greatest integer function, continuity on a closed interval, Intermediate Value Theorem, Approximating tangent line to a graph by secant line, formula for the derivative of a function at a point. |
| Fri. Sep 25 | Quiz 3, The derivative function of f(x), formulas for derivatives of simple functions |
| Mon. Sep 28 | Power rule for derivative, derivative of sin(x), cos(x), quotient and product rules. |
| Wed. Sep 30 | On the homework about continuity, What does the derivative mean in the context of a real life problem - rate of change and instantaneous rate of change; different notations for derivatives; higher order derivatives |
| Fri. Oct 2 | Quiz 4, chain rule; mid-semester evaluations |
| Mon. Oct 5 | More chain rule examples, word problems about rate of change |
| Wed. Oct 7 | On some homework problems, Implicit differentiation |
| Fri. Oct 9 | Quiz 5(take-home), More examples on implicit differentiation, related rates problems |
| Mon. Oct 12 | More related rate problems, When a derivative doesn't exist. |
| Wed. Oct 14 | Local (relative) max, min; global (absolute) max, min; critical numbers, finding global extrema over a closed interval. |
| Fri. Oct 16 | Midterm Exam |
| Mon. Oct 19 | Fall Break! |
| Wed. Oct 21 | Global, local max, min; critical numbers; finding them analytically |
| Fri. Oct 23 | Rolle's Theorem and Mean Value Theorem |
| Mon. Oct 26 | What does the first derivative tell about the function? ( Making a sign chart for the derivative to find where the original function isincreasing/decreasing, and where it has local max and min) |
| Wed. Oct 28 | Concavity of a function, inflection points and the second derivative |
| Fri. Oct 30 | Quiz 6, More on concavity, horizontal asymptotes |
| Mon. Nov 2 | Second derivative test; Limits at infinity - Horizontal asymptotes (end behavior of a function) |
| Wed. Nov 4 | Curve sketching - domain; intercepts; symmetry; sign chart; asymptotes; intervals of increase/decrease (sign chart for the first derivative), local extrema; concavity, inflection points (sign chart for the second derivative); put all of them together on the graph! |
| Fri. Nov 6 | Quiz 7, Optimization |
| Mon. Nov 9 | More optimization problems, introduction to Newton's method |
| Wed. Nov 11 | Formula for Newton's method, review for the exam |
| Fri. Nov 13 | Exam 3 |
| Mon. Nov 16 | Estimating values of a function, differentials and error propagation, relative error |
| Wed. Nov 18 | Antiderivatives, indefinite integrals, basic integrals, differential equations, general solutions, initial value problems |
| Fri. Nov 20 | Quiz 8, Estimating an area under a curve using lower rectangles and upper rectangles |
| Mon. Nov 23 | Sigma notation, exact area under a curve |
| Wed. Nov 25 | Happy Thanksgiving! |
| Fri. Nov 27 | Happy Thanksgiving! |
| Mon. Nov 30 | Riemann Sum, definite integral, examples |
| Wed. Dec 2 | The (First) Fundamental Theorem of Calculus |
| Fri. Dec 4 | Average value of a function, The Second Fundamental Theorem of Calculus |
| Mon. Dec 7 | Quiz 9, Integration by substitution |
| Wed. Dec 9 | Substitution and definite integrals, Numerical integration, trapezoidal integral |
| Fri. Dec 11 | REVIEW |