Calculus

This course consists of two parts:

1. Part 1: Functions of multiple variables

2. Part 2: Differential equations

In Part 1, we extend the student's knowledge of calculus applied to functions depending on one variable to functions depending on two or more variables.

We focus on the operations of differentiation and integration applied to such functions.

In addition, the student's "mathematical toolbox" will be expanded with techniques for working with vectors, taking derivatives and performing integration.

Topics in Part 1 are among others

• Vectors, inner product, cross product;

• Equations of lines and planes;

• Inverse trigonometric functions;

• Differentiation and Integration techniques;

• Functions of multiple variables;

• Partial and directional derivative;

• Extreme values of functions;

• Multiple integrals;

• Coordinate systems.

In Part 2, we focus on differential equations. These are needed during the modeling of physical phenomena in the study of the earth and climate.

We focus on solving some specific types of differential equations.

Topics in Part 2 are among others

• Complex numbers;

• Direction field;

• First and second order differential equations;

• Taylor polynomials.

Examination dates and Examination method

• For each part, there is optional homework in Grasple which is part of a bonus regulation;

• For Part 1, the exam is at the end of Period 1;

• For Part 2, the exam is in the middle of Period 2;

• The resit for Part 1 and for Part 2 is at the end of Period 2;

All examination will be administered via a digital examination software in a PC hall at the TU Delft. To participate in an exam, the student needs to be present in the PC hall. Every exam consist of a written component.

Permitted materials during examination

During each examination of this course, the student may use the following permitted materials.

Permitted materials which the student is responsible for:

• Pen and Pencil;

• Ruler, protractor triangle (geodriehoek) and compass.

Other permitted materials which is provided at the examination:

• Formula sheet (https://prime.pages.ewi.tudelft.nl/formula-sheets/AESB1211/AESB1211.html);

• Scrap paper;

• Attendance and Answer form.

Other materials are not permitted. This includes the following:

• Calculator;

• Pencil pouch;

• Smart devices (including mobile phones, smart watches);

• Own notes.

These materials should not be present on the table and should be stored.

Final grade for ECTB1140

In case there are multiple recorded results for a specific part of the course, then the highest valid result will be considered. According to the RGBoE, each recorded result has unlimited validity.

To receive a final grade for this course (ECTB1140), the student needs to meet the following criteria:

• For Part 1, a grade of minimum 5,0 (not rounded to wholes and halves) is earned;

• For Part 2, a grade of minimum 5,0 (not rounded to wholes and halves) is earned;

If both the criteria is met, then the student will receive a final mark, computed as the average of the grades for Part 1 and Part 2.

The final mark will be rounded to wholes and halves. The student passed the course if the final mark is minimum 6,0 (after rounding to wholes and halves). The least average for passing the course is 5,75 (not rounded).

Grade for ECTB1140 Part 1 (short Part 1)

• Let D1 be the result of the exam of Part 1 at the end of Period 1 (1-10 scale, rounded to tenths);

• Let H1 be the result of the resit of Part 1 at the end of Period 2 (1-10 scale, rounded to tenths);

• Let G1 be the result of the homework of Part 1 before the exam of Part 1 at the end of Period 1 (0-10 scale, rounded to tenths).

The grade E1 for Part 1 in Period 1 is computed according to the following criteria:

• If D1 >= 5,0, then E1 = MAX{ 0,85 * D1 + 0,15 * G1; D1};

• If D1 < 5,0, then E1 = D1.

The grade E1h for Part 1 in Period 2 is computed according to the following criteria:

• It holds E1h = H1.

The result G1 is only valid during the academic year the grade is obtained.

Grade for ECTB1140 Part 2 (short Part 2)

• Let D2 be the result of the exam of Part 2 in the middle of Period 2 (1-10 scale, rounded to tenths);

• Let H2 be the result of the resit of Part 2 at the end of Period 2 (1-10 scale, rounded to tenths);

• Let G2 be the result of the homework of Part 2 before the exam of Part 2 in the middle of Period 2 (0-10 scale, rounded to tenths).

The grade E2 for Part 2 in Period 2 is computed according to the following criteria:

• If D2 >= 5,0, then E2 = MAX{ 0,85 * D2 + 0,15 * G2; D2};

• If D2 < 5,0, then E2 = D2.

The grade E2h for Part 2 in Period 2 is computed according to the following criteria:

• It holds E2h = H2.

The result G2 is only valid during the academic year the grade is obtained.