Georgia Tech MATH 1551 Differential Calculus: Study Guide, Practice
A study guide for Georgia Tech MATH 1551 (Differential Calculus): limits of functions and sequences, derivatives and applications, with practice.
Georgia Tech Updated 3 min read
At a glance
- Course code
- MATH 1551
- Credits
- 2 credit hours
- Covers
- Differential calculus and its applications, plus the theory of limits for functions and sequences
- Credit restrictions
- No credit for both MATH 1551 and MATH 1501, MATH 1503 or MATH 1550
- Related course
- MATH 1550 (Introduction to Differential Calculus, 3 credit hours)
- Practice here
- Calculus 1, from limits through applications of derivatives
On this page
Georgia Tech MATH 1551 is Differential Calculus, a 2-credit-hour course that covers the derivative half of a traditional first calculus course. Georgia Tech splits single-variable calculus in two, with integration handled separately in MATH 1552. This guide maps every MATH 1551 topic to free practice, so you can learn each idea by solving problems with instant feedback.
What MATH 1551 covers
The Georgia Tech catalog describes MATH 1551 as differential calculus with its applications, together with the underlying theory of limits for both functions and sequences. Credit is not awarded for both MATH 1551 and MATH 1501, MATH 1503 or MATH 1550.
Compared with a standard Calculus 1 course, MATH 1551 covers limits, continuity, derivatives and their applications, but stops before antiderivatives and the definite integral. The inclusion of sequences is worth noticing: limits of sequences, such as \lim_{n \to \infty} \frac{n}{2n + 1}, are part of the course rather than waiting for a series unit.
MATH 1551 topic map
| MATH 1551 topic | Practice | Read |
|---|---|---|
| Limits of functions | What is a limit? | How to evaluate limits, limit laws |
| Indeterminate forms | Factor and cancel | Squeeze theorem |
| Limits at infinity | Limits at infinity | Limits at infinity |
| Limits of sequences | Sequences and their limits | Limits at infinity |
| Continuity | Continuity | Continuity, Intermediate Value Theorem |
| The derivative | The limit definition | Limit definition of the derivative |
| Differentiation rules | Mixed rules practice | Power rule, quotient rule |
| Chain rule and implicit differentiation | Chain rule: any function | Chain rule, implicit differentiation |
| Extrema and curve sketching | Critical points | Curve sketching, Extreme Value Theorem |
| Optimization and related rates | Optimization | Optimization problems, related rates |
| Mean Value Theorem and linear approximation | Tangent lines at work | Mean Value Theorem |
| L'Hôpital's rule | L'Hôpital's rule | L'Hôpital's rule |
MATH 1551 vs MATH 1550 and the rest of the sequence
| Course | Credit hours | What it covers |
|---|---|---|
| MATH 1550 (Introduction to Differential Calculus) | 3 | Differential calculus, applications and the theory of limits |
| MATH 1551 (Differential Calculus) | 2 | Differential calculus, applications and the theory of limits for functions and sequences |
| MATH 1552 (Integral Calculus) | 4 | Integrals, integration techniques, improper integrals, infinite series |
| MATH 2551 (Multivariable Calculus) | 4 | Several variables through vector analysis |
The catalog lists MATH 1550 and MATH 1551 as mutually exclusive for credit. For the integral half of single-variable calculus see the MATH 1552 guide, and for several variables see the MATH 2551 guide.
Example problems at the MATH 1551 level
1. A 0/0 limit. Factor and cancel:
2. The limit of a sequence. Divide the top and bottom by n:
3. A quotient rule derivative. Differentiate f(x) = \frac{x}{x^2 + 1}:
So f has critical points at x = \pm 1, a maximum of \frac{1}{2} at x = 1 and a minimum of -\frac{1}{2} at x = -1.
How to do well in Georgia Tech MATH 1551
- Keep up every week. A 2-credit-hour course moves quickly. Ten minutes a day on limits practice beats a weekend of cramming.
- Understand limits, not just how to compute them. The catalog stresses the theory of limits, so be ready to explain why a limit exists or fails to, using one-sided limits and the squeeze theorem.
- Make the derivative rules automatic. Use the calculus formula sheet while practicing, then try problems without it.
- Watch for classic slips. Our list of common calculus mistakes covers sign errors and chain rule omissions.
- Simulate exams with timed practice exams before each test.
Tip: for a sequence limit like \frac{n}{2n+1}, the same "divide by the highest power" trick from limits at infinity works every time.
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What is a limit?
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