Rutgers Math 135 (01:640:135) Calculus I: Study Guide and Practice
A study guide for Rutgers Math 135, Calculus I for the Life and Social Sciences: limits, derivatives, applications and basic integration, with practice.
Rutgers University Updated 3 min read
At a glance
- Course code
- 01:640:135 (Math 135)
- Credits
- 4
- Offered
- Fall, spring and summer
- Prerequisites
- Math 112 or Math 115, or placement
- Covers
- Limits and continuity, the derivative and tangent lines, applications of the derivative, basic integration
- Who takes it
- Many biological and social science majors, and Rutgers Business School students
- Practice here
- Calculus 1
On this page
Rutgers Math 135 (01:640:135, Calculus I for the Life and Social Sciences) is the Calculus I course at Rutgers New Brunswick intended for many biological and social science majors, and Rutgers Business School currently requires it. It is a full introduction to calculus with a focus on rates of change and their applications. This guide maps each Math 135 topic to a lesson you can practice with instant feedback.
What Rutgers Math 135 covers
The Rutgers math department describes Math 135 as an introduction to calculus covering limits and continuity, the derivative and tangent lines, applications of the derivative, and basic integration.
In standard terms, that is Calculus 1, with integration covered at an introductory level. On PracticeCalculus it lines up with the Calculus 1 path from limits through the integrals unit. Growth models and rates of change in biology and economics make the rate-of-change lessons especially useful.
Math 135 topic map
| Math 135 topic | Practice | Read |
|---|---|---|
| Functions, exponentials and logs | Exponentials and logarithms | Exponential functions, natural logarithm |
| Limits | What is a limit? | How to evaluate limits |
| Continuity | Continuity | Continuity |
| Rates of change | Average rate of change | Limit definition of the derivative |
| The derivative and tangent lines | Tangent lines | Power rule |
| Derivative rules | Product rule | Product and quotient rules, chain rule |
| Exponential growth | Chain rule: e and ln | Derivatives of exponential and log functions |
| Applications: graphs and optimization | Optimization | Optimization problems, curve sketching |
| Basic integration | The reverse power rule | Antiderivatives |
| Definite integrals and net change | Net change and displacement | Fundamental Theorem of Calculus |
Math 135 vs Math 151
| Question | Math 135 | Math 151 |
|---|---|---|
| Intended for | Many biological and social science majors, Rutgers Business School | Mathematical and physical sciences, School of Engineering |
| Credits | 4 | 4 |
| Next course | Math 136, or Math 152 (not recommended) | Math 152 |
| Leads to Math 251? | Not through Math 136 | Yes, through Math 152 |
The department's advice is simple: if your major might need Math 152 or Math 251, take Math 151. If you are unsure, ask an adviser in your major. Also note that students who fail Calculus I (135 or 151) twice cannot take it again at New Brunswick without an approved appeal.
Example problems at the Math 135 level
1. Marginal cost. If C(q) = 0.5q^2 + 10q + 100 dollars, then C'(q) = q + 10. At q = 20 units, the marginal cost is C'(20) = 30 dollars per unit.
2. Exponential growth rate. A population grows as P(t) = 500e^{0.04t}. Then
so at t = 0 it is growing by 20 individuals per year.
3. Net change from a rate. If water flows in at r(t) = 2t + 1 liters per minute, the amount added in the first 3 minutes is
How to do well in Math 135
- Master exponentials and logs. Growth and decay models are everywhere in life and social science applications. The exponentials and logarithms warm-up is a good start.
- Always state units. A derivative is a rate, so its units are "output per input". Writing units catches many setup mistakes.
- Drill the rules with the formula sheet open at first, then closed.
- Review common calculus mistakes and take timed practice exams before each midterm.
Tip: "marginal" in economics just means "derivative". Marginal cost, revenue and profit are C', R' and P'.
Practice it now
Average rate of change
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