MAT-275 at Southern New Hampshire University continues MAT-225 and deepens single-variable calculus. The catalog lists new integration techniques (substitution, integration by parts, partial fractions and integration tables), infinite series, and parametric curves and polar coordinates.
Students often find it a step up because success depends on choosing the right technique among several. Series add another shift: the question moves from computing a value to deciding whether an infinite sum has a value at all.
Course at a Glance
| Item | Details |
|---|---|
| University | Southern New Hampshire University |
| Course code | MAT-275 |
| Credits | 3 |
| Level | Undergraduate |
| Prerequisite | MAT-225 with a grade of C or better |
| Offering | SNHU lists it as offered every spring term |
| Typical work | Problem sets on techniques, convergence and curves (general; check your term) |
What MAT-275 Covers
| Topic | Idea |
|---|---|
| Integration techniques | Substitution, integration by parts, partial fractions, tables |
| Estimating integrals | Using series to evaluate and estimate integrals |
| Infinite series | Adding infinitely many numbers and deciding when the sum is finite |
| Functions as series | Representing exponential, trigonometric and logarithmic functions as polynomial-like series |
| Parametric curves | Describing motion with a parameter |
| Polar coordinates | Describing curves with distance and angle |
Key Concepts Explained
Integration by Parts
Integration by parts reverses the product rule: the integral of u dv equals uv minus the integral of v du. Choose u to be the part that gets simpler when differentiated.
Example: For the integral of x e^x dx, let u = x and dv = e^x dx. Then du = dx and v = e^x, so the result is x e^x - e^x + C.
Geometric Series
A geometric series with first term a and ratio r has sum a / (1 - r) when |r| is less than 1, and it diverges otherwise.
Example: 1 + 1/2 + 1/4 + 1/8 + ... has a = 1 and r = 1/2, so the sum is 1 / (1 - 1/2) = 2.
Parametric Curves
If x = t and y = t squared, eliminating t gives y = x squared, a parabola. The parameter t also tells you the direction and speed of traversal, which a plain equation does not.
Typical Assignments and How to Approach Them
| Assignment type | What it tests | How to approach it |
|---|---|---|
| Technique drills | Choosing and executing the right method | Look at the integrand and match it to a pattern before starting |
| Convergence problems | Testing series | Name the test, check its conditions, then state a conclusion |
| Series approximation tasks | Using series to estimate values | State the number of terms and the approximate error you accept |
| Curve problems | Parametric and polar work | Sketch from a table of parameter values and mark direction |
Picking an Integration Technique
The key skill is recognition. Use this table as a first pass, then confirm by trying the method on a simple case:
| If the integrand looks like | Try |
|---|---|
| A function times its own derivative | Substitution |
| A polynomial times e^x, sin x or cos x | Integration by parts |
| A rational function with a factorable denominator | Partial fractions |
| A standard form in your table | Integration tables |
Studying Series
For each series, ask three questions in order: does the term go to zero, which test fits the pattern, and are the conditions of that test satisfied? Writing the test name beside your conclusion earns marks for reasoning.
Two Worked Integrals
Substitution: the integral of 2x cos(x^2) dx. Let u = x^2, so du = 2x dx. The integral becomes cos u du, which is sin u + C = sin(x^2) + C.
Partial fractions: 1/(x^2 - 1) = (1/2)[1/(x - 1) - 1/(x + 1)], so the integral is (1/2) ln|x - 1| - (1/2) ln|x + 1| + C.
Check: Differentiate each answer. The first returns 2x cos(x^2); the second returns 1/(x^2 - 1).
Polar Basics
Polar coordinates use distance r and angle theta, with x = r cos(theta) and y = r sin(theta). The equation r = 2 describes a circle of radius 2 centered at the origin, which is much simpler than writing it in x and y.
Where Students Get Stuck
- Wrong technique. Practice sorting problems by type before solving them.
- Dropping constants. Include + C for indefinite integrals and check limits for definite ones.
- Testing series. The test must match the pattern, and its conditions must be checked.
- Polar and parametric sketches. Plot enough points and note direction.
Study Tips for MAT-275
- Keep a technique sheet with one example each.
- Check integrals by differentiating your answer.
- Do mixed sets that do not tell you the technique.
- Write the name of each convergence test next to the series it handles.
How We Help with MAT-275
Send the problem set, your notes and your working. A maths tutor can explain each technique, prepare fully worked solutions, or find where your reasoning slips.
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Frequently Asked Questions
SNHU lists a grade of C or better in MAT-225.
SNHU's catalog says every spring term; plan ahead.
Integration techniques, infinite series, representing functions as series, parametric curves and polar coordinates.
Many students find the range of techniques and the series material more demanding.
Both continue calculus with integration and series, but they are separate courses with separate requirements.
Yes. We review the technique and each step and explain any corrections.