MS-A0111: Differential and Integral Calculus 1
| Course name | Differential and Integral Calculus 1 |
|---|---|
| Course code | MS-A0111 |
| Abbreviation | Calc1 |
| Period | I |
| Lecturer | No idea, used to be Milo |
Description
Differential and Integral Calculus 1 is a 5 ECTS introductory calculus course offered by the Department of Mathematics and Systems Analysis. It covers the foundational tools of single-variable calculus and an introduction to differential equations. After the course, students master the most important properties, calculation methods, and applications of the derivative and the integral; can solve first-order differential equations in the linear and separable cases; and can solve linear second-order differential equations with constant coefficients. The course also covers sequences, series, and power series. It is one of the most fundamental courses taken in the first year of engineering and science programmes at Aalto.
Course material
Official material
The official textbook is Adams & Essex, Calculus: A Complete Course, 7th Edition (Pearson). Chapters are assigned per week and correspond directly to the lecture content. Weekly exercise sheets are distributed via MyCourses. Students are expected to both read the textbook and work through the problem sets independently in addition to attending lectures.
Extra material
Paul’s Online Math Notes (tutorial.math.lamar.edu) is a freely available reference widely used by students for alternative explanations and extra practice problems. For those who prefer video, the MIT 18.01 Single Variable Calculus lectures on OpenCourseWare are excellent. The Zulip discussion forum set up for the course is also useful — questions from previous years remain searchable and often address common points of confusion.
Contents and workload
Overall workload, balls
Overall workload 2/5. The course runs during the first period (approximately 7 weeks) and is 5 ECTS, making it similarly intense to MS-A0011. Expect around 12–14 hours per week. The first few weeks covering limits and derivatives are manageable, but the pace increases significantly when integration techniques and series are introduced. The final weeks on differential equations are considered the most challenging by most students. Weekly exercise submission is mandatory for a portion of the grade.
Weekly contents
| Week | Topics |
|---|---|
| 1 | Real numbers, functions, and limits; $\varepsilon$–$\delta$ definition introduced informally; continuity. |
| 2 | The derivative; rules of differentiation (product, quotient, chain rule); derivatives of elementary functions. |
| 3 | Applications of the derivative; mean value theorem; increasing/decreasing functions; extrema. |
| 4 | The integral; antiderivatives; the fundamental theorem of calculus; definite and indefinite integrals. |
| 5 | Integration techniques; substitution; integration by parts; partial fractions. |
| 6 | Sequences and series; convergence tests; power series; Taylor series. |
| 7 | First-order differential equations (separable and linear); second-order linear ODEs with constant coefficients; revision. |
Practicalities
The course is completed via weekly exercise submissions and a final written exam. The exam is closed-book and covers all topics from the course; a formula sheet may or may not be provided depending on the lecturer. Weekly exercises contribute to the final grade (the weight varies by year). Lectures are twice a week and exercise sessions once or twice a week. The Laskutupa drop-in help centre is available throughout the semester and is particularly busy in the weeks before the exam.
Related courses
Official prerequisites
High school mathematics. Students are expected to be comfortable with trigonometry, algebraic manipulation, and the concept of a function.
Additional prerequisites
A solid grasp of high school-level limits and differentiation (if covered) makes the first weeks much smoother. Students from the short mathematics track in high school (lyhyt matematiikka) may face a steeper initial curve.
More like this
- MS-A0211 Differential and Integral Calculus 2 — the direct continuation covering multivariable calculus.
- MS-A0011 Matrix Algebra — the companion linear algebra course, typically taken in the same academic year.
- PHYS-C0110 Mechanics — uses calculus extensively; taking Calc 1 concurrently or before Mechanics is beneficial.
- MS-A0311 Vector Calculus — further mathematical tools for physics and engineering students.