 Mika Seppälä: Video on Riemann Sums and Definite Integrals

This is an online course on integral calculus and focuses on defining integration, techniques, as well as improper integrals.

### Kuvaus

Course is part of bachelor degree program in mathematical sciences and therein basic studies. It is second in a series of online Calculus courses. The collection of the three courses

• MAT11006: Calculus 1A: Limits and Differentiation
• MAT11007: Calculus 1B: Integration
• MAT11008: Advanced Calculus

correspond to the collection of the three Finnish analysis courses

• MAT11003 Raja-arvot

However, no single course in either collection can substitute a course from the other.

The course MAT11006: Calculus 1A: Limits and Differentiation is a prerequisite for taking this course.

Online English course MAT21002 Series, or its Finnish equivalent "Sarjat" continues the theme of the calculus courses.

After successfully completing this course students will

• Understand what is meant by an antiderivative of a function, and find antiderivatives of basic functions
• Be able to form Riemann sums for functions on an interval
• Understand the concept of definite integral as a limit of Riemann sum
• Be familiar with the Fundamental Theorem of Calculus, explain why it holds, and use it in applications
• Use several integration techniques, such as integration by substitution, partial fraction decompositions, and integration by parts
• Apply integration in finding area under the graph of a function, calculating volumes and surface areas of solids of revolution as well as lengths of parametric curves
• Understand concept of improper integrals, determine whether they converge and calculate their values

This course can be taken after the course MAT11006 Calculus 1A: Limits and Differentiation.

This course is organized in the second period in the fall term.

Course covers the following main topics

1. Antiderivatives
2. Definite integrals and Riemann sums
3. Fundamental Theorem of Calculus
4. Integration techniques
5. Applications of integration: areas, volumes, lengths
6. Improper integrals and their convergence

All necessary study material can be found in the course area. Standard Calculus text books, such as Adams' or Stewart's Calculus books can be used as side material among others.

Studying in this course follows a weekly cycle. Each week students are expected to:

1. Watch the prerecorded lectures or read the text allocated for the next workshop at the class Moodle site.
2. Solve quiz problems. They will help to prepare for the workshops.
3. Submit solutions to workshop problems by Wednesday evening.
4. Grade and give feedback to other students’ workshop submissions by Sunday evening.
5. Also ask questions, hints for solving problems etc. in the discussion forum.

Continuous formative assessment takes place throughout the course by weekly quizzes and workshops. These will give homework extra credit maximum of 5 points.

Final paper and pencil exam will measure comprehensively the learning goals as specified in section 9.

Scale 1-5 of grades will be used. Passing course with grade 1 will require approximately half of the points of the exam and for the best grade approximately 5/6 of the exam points are required. Homework extra credit points will be added to the exam points.

This is an online course. All course material and activities can be found on the online course area. There is a final proctored paper and pencil exam at the end of the course.