Course Syllabus

Draft Syllabus

Course Description

This course delves into foundational concepts of differential and integral calculus. These include functions, limits and derivatives, integrals, as well as applications of differentiation and integration. Throughout the course, students apply these concepts utilizing real-world examples, while developing skills in mathematical reasoning and problem-solving.

Course components

This course covers chapters 1-6 of the textbook indicated below. In more detail, the course covers the following sections and subsections:

1. Functions and Models

1.2. Mathematical Models and Essential Functions
1.4. Exponential Functions
1.5. Inverse Functions and Logarithms

2. Limits and Derivatives

2.1. The Tangent and Velocity Problems
2.2. The Limit of a Function
2.3. Calculating Limits Using the Limit Laws
2.4. The Precise Definition of a Limit
2.5. Continuity
2.6. Limits at Infinity; Horizontal Asymptotes
2.7. Derivatives and Rates of Change
2.8. The Derivative as a Function

3. Differentiation Rules

3.1. Derivatives of Polynomials and Exponential Functions
3.2. The Product and Quotient Rules
3.3. Derivatives of Trigonometric Functions
3.4. The Chain Rule
3.5. Implicit Differentiation
3.6. Derivatives of Logarithmic Functions
3.7. Rates of Change in the Natural and Social Sciences
3.8. Exponential Growth and Decay
3.9. Related Rates
3.10. Linear Approximations and Differentials
3.11. Hyperbolic Functions

4. Applications of Differentiation

4.1. Maximum and Minimum Values
4.2. The Mean Value Theorem
4.3. How Derivatives Affect the Shape of a Graph
4.4. Indeterminate Forms and l’Hospital’s Rule
4.5. Summary of Curve Sketching
4.6. Graphing with Calculus and Calculators
4.7. Optimization Problems
4.8. Newton’s Method
4.9. Antiderivatives

5. Integrals

5.1. Areas and Distances
5.2. The Definite Integral
5.3. The Fundamental Theorem of Calculus
5.4. Indefinite Integrals and the Net Change Theorem
5.5. The Substitution Rule

6. Applications of Integration

6.1. Areas between Curves
6.2. Volumes
6.3. Volumes by Cylindrical Shells
6.4. Work
6.5. Average Value of a Function

Learning Objectives

Upon successfully completing the course, the student will be able to: 

• Apply fundamental concepts of differential and integral calculus during mathematical reasoning
• Apply concepts of differential and integral calculus to real-life problems within the natural sciences, social sciences or engineering
• Develop the ability to communicate mathematical ideas clearly and effectively, using appropriate mathematical notation and language

Faculty

TBA

Readings

Field Studies

We will have two course-integrated field studies to learn how the course topics could be applied in relevant industries and in academic research.

Field studies may include:

Visit to Middelgrunden Windfarm

Visit to the Niels Bohr Institute 

Guest Lecturers

Guest lecturers may be invited to talk about topics of particular interest to students.

Approach to Teaching

The course consists of interactive lectures, class exercises, and problem-solving. Discussion of applications is included, especially during field studies.

DIS Accommodations Statement 

Your learning experience in this class is important to me.  If you have approved academic accommodations with DIS, please make sure I receive your DIS accommodations letter within two weeks from the start of classes. If you can think of other ways I can support your learning, please don't hesitate to talk to me. If you have any further questions about your academic accommodations, contact Academic Support acadsupp@dis.dk. 

Expectations of the Students

• You should participate actively during lectures, discussions, group work, and exercises.
• Laptops may be used for note‐taking, fact‐checking, or assignments in the classroom, but only when indicated by the instructor. At all other times, laptops and electronic devices should be put away during class meetings.
• Readings must be done prior to the class session. 
• In addition to completing all assignments and exams, you need to be present, arrive on time, and actively participate in all classes and field studies to receive full credit. Your final grade will be affected, adversely, by unexcused absences and lack of participation. Your participation grade will be reduced by 10 points (over 100) for every unexcused absence. Remember to be in class on time!
• Classroom etiquette includes being respectful of other opinions, listening to others and entering a dialogue in a constructive manner.
• You are expected to ask relevant questions in regards to the material covered.
• Excuses for any emergency absences must be given beforehand. It is the responsibility of the student to make up any missed coursework.

Evaluation

To be eligible for a passing grade in this class, all of the assigned work must be completed.

You are expected to turn in all assignments on the due date. If an assignment is turned in after the due date, your assignment grade will be reduced by 10 points (over 100) for each day the submission is late. 

Grading

Active participation: Includes attendance, preparation for lectures and other sessions, active participation in learning activities, class discussions, group work and problem solving. It also includes active participation during field studies and presentation of reflections on how they are related and relevant within the context of the course.

Assignments:  Take home and in class assignments will be posted on Canvas. Students are allowed to work in groups to complete their homework. A pdf scan or clear photo of their work must be submitted on Canvas. Late submissions of homework will be deducted by 10 points for each day the homework is late.

Midterm Exam: Mid-way through the semester, you will take an exam that covers all topics covered thus far in the course. 

Exam: At the end of the semester, you will take an exam that covers all topics from the course. 

Academic Regulations

Please make sure to read the Academic Regulations on the DIS website. There you will find regulations on:

• Course Enrollment and Grading
• Academic Expectations and Honor Code

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