ASU MAT 265 Calculus for Engineers I: Study Guide and Practice
A study guide for ASU MAT 265 Calculus for Engineers I: limits, continuity, derivatives of one variable and an introduction to integration, with practice.
Arizona State University Updated 3 min read
At a glance
- Course code
- MAT 265
- Credit hours
- 3
- General studies
- Mathematical Studies (MATH / MA)
- Covers
- Limits and continuity, differential calculus of functions of one variable, an introduction to integration
- Offered by
- School of Mathematical and Statistical Sciences
- Next course
- MAT 266 Calculus for Engineers II
- Practice here
- Calculus 1
On this page
ASU MAT 265, Calculus for Engineers I, is the first course in Arizona State University's engineering calculus sequence, offered by the School of Mathematical and Statistical Sciences. It is where many engineering and science students meet limits and derivatives at ASU. This guide maps every MAT 265 topic to a lesson you can practice with instant feedback.
What ASU MAT 265 covers
The ASU course catalog describes MAT 265 in one line: limits and continuity, differential calculus of functions of one variable, and an introduction to integration. It carries 3 credit hours and counts toward the Mathematical Studies general studies requirement.
That is a standard Calculus 1. Most of the semester is about derivatives, their rules and their applications, with integration introduced at the end and developed further in MAT 266. On PracticeCalculus it matches the Calculus 1 path from limits through the integrals unit.
MAT 265 topic map
| MAT 265 topic | Practice | Read |
|---|---|---|
| Limits | What is a limit? | What is a limit?, limit laws |
| One-sided and infinite limits | One-sided and infinite limits | How to evaluate limits |
| Continuity | Continuity | Continuity, piecewise functions |
| The derivative | The limit definition | Limit definition of the derivative |
| Derivative rules | Chain rule: any function | Chain rule, product and quotient rules |
| Trig, exponential and log derivatives | Sine, cosine and tangent | Derivatives of trig functions |
| Implicit differentiation | Implicit differentiation | Implicit differentiation |
| Related rates | Related rates | Related rates |
| Extrema and optimization | Optimization | Optimization problems |
| L'Hôpital's rule | L'Hôpital's rule | L'Hôpital's rule |
| Introduction to integration | Evaluating definite integrals | Fundamental Theorem of Calculus |
ASU calculus sequences
| Course | Credit hours | Catalog topics |
|---|---|---|
| MAT 265 Calculus for Engineers I | 3 | Limits, continuity, derivatives, intro to integration |
| MAT 266 Calculus for Engineers II | 3 | Integration methods, applications, improper integrals, Taylor series |
| MAT 267 Calculus for Engineers III | 3 | Vector-valued functions, partial derivatives, multiple integration |
| MAT 270, 271, 272 Calculus with Analytic Geometry I, II, III | 4 each | The same ground at 4 credits, adding sequences and series and vector analysis |
| MAT 210 Brief Calculus | 3 | Applied derivatives and integrals of elementary functions |
Which sequence you take depends on your major, so check your degree map before registering.
Example problems at the MAT 265 level
1. Continuity of a piecewise function. Find a so that f(x) = x^2 for x < 2 and f(x) = ax for x \ge 2 is continuous. The left limit at 2 is 4 and f(2) = 2a, so 2a = 4 and a = 2.
2. Related rates. A balloon's radius grows at 2 cm/s. Since V = \frac{4}{3}\pi r^3, \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}. When r = 5 cm:
3. A first definite integral.
How to do well in MAT 265
- Master limits early. Continuity and the derivative are both defined by limits. The limits unit builds them step by step.
- Make derivative rules automatic. Drill the power rule, product rule, quotient rule and chain rule until they take seconds.
- Use a fixed method for word problems. Draw, name variables, write the equation, differentiate, then substitute. It works for both related rates and optimization.
- Keep the formula sheet handy, review common calculus mistakes, and take timed practice exams before each test.
Tip: for continuity questions about piecewise functions, set the left limit, the right limit and the function value equal at the break point.
Practice it now
What is a limit?
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