Math 34B
Calculus for the Social and Life Sciences
Integrals can be interpreted from a number of viewpoints. Please scroll down to view the section appropriate to your question.
Interactive | Introduction to Integrals |
Interactive | Determing definite and indefinite integrals using antiderivatives. |
Video - 10:28 | Intro to the concept of area under a curve and its meaning |
Video - 3:04 | Definite integral as area under the curve and its interpretation (rectangle) |
Video - 2:40 | Definite integral as area under the curve and its interpretation (triangle) |
Video - 2:59 | Definite integral as area under the curve and its interpretation (trapezoid) |
Video - 3:43 | Intro to indefinite integral and antiderivatives |
Text | Intro to indefinite integral and some basic properties |
Interactive | Visualization of antiderivative |
Video - 3:46 | Examples on the power rule |
Video - 3:28 | Examples on the power rule (with square roots) |
Video - 2:18 | Examples on the power rule (for polynomials) |
Video - 4:04 | Examples on the power rule (with natural log) |
Video - 2:52 | Examples on the power rule (with fractions) |
Interactive | Do-it-all mathematics tool | Type "Integral of ____________" |
Video - 3:28 | FTC part II and an example |
Interactive | FTC some interactive examples |
Interactive | FTC with interactive applet |
Interactive | FTC with some interactive elements |
Text | Explanation and proof for the FTC (for more advanced students) |
Video - 10:20 | FTC with examples |
Video - 9:51 | Examples of taking definite integrals | Skipped Parts 1-3, as they seemed unnecessarily confusing |
Text | Introduction to the definite integral | 34B students may ignore Example 6 and 7 |
Text | Computing definite integrals using FTC and examples | 34B students may ignore Example 3 |
Interactive | Using a Riemann sum to estimate area under the curve |
Text | Intro to definite integral as area under the curve |
Interactive | Interactive applets demonstrating Riemannian sums |
Video - 3:55 | Example on finding the average value of a function |
Video - 3:33 | An example on average value of a function |
Video - 7:31 | Intro to average value and examples |
Interactive | Graphs sine/cosine/exponential functions with user-inputted parameters |
Interactive | Plot sine curves based on user-inputted amplitude, period, and phase shift |
Video - 9:54 | Two examples on graphing trig functions |
Interactive | Exercises on sine and cosine graphs |
Text | The six basic trigonometric functions and their graphs | It has three pages total. |
Video - 8:22 | Graphing trig functions via graph transformations |
Interactive | Applet demonstrating how derivative of sin(t) is cos(t) |
Video - 9:56 | Intro to amplitude and period of a sine/cosine function |
Video - 9:30 | Intro to horizontal and vertical translations of a sine/cosine function |
Video - 10:02 | Summary of sine/cosine waves and examples on how to graph them |
Video - 3:45 | How to graph a sine wave from its formula |
Video - 3:34 | How to graph a sine wave from its formula |
Video - 4:30 | How to find the formula of a sine wave from the graph |
Video - 7:24 | How to find the formula of a sine wave from the graph | You can ignore the second half of the video when he uses the cosine formula. |
Video - 6:23 | Examples on integrals of trig functions |
Video - 8:48 | Product rule examples | Last example uses chain rule, which you may not know. |
Text | Product rule explanation and examples | Also introduces quotient rule, which you may not know. |
Video - 3:57 | Product rule example (with e^x) |
Text | Examples of finding max/min | Last method is second derivative test |
Text | Finding inflection points |
Text | Using the second derivative test to find extrema |
Video - 8:41 | Introduction to second derivative test |
Video - 7:10 | Second derivative test example |
Video - 6:10 | Shows power series for e^x | After 4:00 begins covering material not covered in 34B. |
Interactive | Demonstrates approximating functions by power series | e^x is #3 in the drop down list |
Video - 12:11 | Discusses how to approximate functions by their power series | Goes more in-depth than what is covered in 34B |
Text | Supplementary material to 34B CLAS groups on diff eqn |
Interactive | Gives slope field and sample solutions to growth/decay and logistic equations |
Text | Introduction and examples for growth/decay |
Text | In depth explanation of Newton's Law of Cooling |
Video - 8:12 | Introduction to differential equations |
Video - 8:07 | Introduction to growth and decay differential equations |
Video - 8:25 | Introduction to Newton's Law of Cooling and examples |
Interactive | Step by step explanation of slope fields and isoclines |
Interactive | Interactive applet to example slope fields |
Interactive | Interactive applet that plots example slope fields and isoclines |
Video - 9:01 | Intro to slope fields and examples |
Text | Some examples done by CLAS |
Interactive | Interactive applet that approximates solutions using Euler's Method |
Text | In depth look at Euler's Method | Might be too advanced for 34B - for adventurous students only! |
Video - 11:11 | Introduction to functions of two variables and partial derivatives | Continues in next video |
Text | Tangent plane formula |
Video - 9:28 | Explanation of Rule of 72 |
Text | Designers of B-2 stealth bomber make calculus error, design bomber to minimumize fuel efficiency |
Text | Explanation of how exponential and logistic differential equations model population growth in "simple" settings |