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Exam schedule
Exam schedule
Winter-Semester 24/25
Winter-Semester 24/25
- Exam: 20.09.2024
Seqences and Series:
Relevant exercises (Rhyn): Section 1, subsection a) Exercises 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, subsection b) Exercises 14, 15, 16, 19, 20, 21, 22, 24, 25, 27, subsection d) Exercises 84, 87, 88, 90, 96, 97
Learning Goals:
To know the concept of a sequence.
Be able to distinguish between the explicit and recursive representation of a sequence.
Be able to formulate the explicit and recursive representation of an easy sequence, where a couple of first terms are given.
To know the concept of the sequence of the n-th partial sums of a given sequence, be able to read and use the summation sign correctly.
To know how sequences can be represented graphically, be able to draw a given sequence into a coordinate system.
To know and to be able to apply the concept of arithmetic and geometric sequences and their explicit and recursive representations, to know and apply the corresponding formulas for finite arithmetic and geometric sums.
To understand the concept of a limit for a sequence, to know and describe the difference between convergent and divergent sequences, to know and describe the different cases of divergences for a sequence, to know and classify the notions of (strict) monotonically increasing and decreasing for sequences.
To know and be able to apply the formal definition of the limit of a convergent sequence (ε-definition).
To know and be able to apply the algebra of limits for sequences, be able to use the limit-sign correctly.
To know and be able to apply the formula for a geometric series, to decide whether a geometric series is convergent or not.
2. Exam: 13.12.2024
2. Exam: 13.12.2024
Differential Calculus I:
Relevant exercises (Rhyn): Section 2, subsection d), Exercises 18, 19, 21, 22, 23, 24; Section 3, subsection a), Exercises 1, 2, 3, 4a), 5, 6, 7, 9, 10, 14, 15, 16; Section 5, subsection a), Exercises 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, subsection b), Exercises 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22; Section 8, Exercises 8, 9, 10, 11, 12, 13, 14.
Learning Goals:
To know and understand the concept of a differential quotient and the difference to a difference quotient.
To be able to compute the derivative of an elementary function by using the differential quotient with the h-method and usual difference method.
To be able to determine the equation of the tangent and normal to the graph of a given function at some point by using differential calculus.
To be able to apply the derivation rules (constant rule, summation rule, power rule, product rule, quotient rule, chain rule) to various functions in order to compute its derivative.
To be able to apply the derivation rules to polynomial, power, trigonometric, exponential and logarithmic functions.
To be able to compute the intersection angle between two functions at their intersections points.
To be able to recognize and apply the trick for logarithmic differentiation.
Summer-Semester 24/25
Summer-Semester 24/25
3. Exam: 28.03.2025
3. Exam: 28.03.2025
Integral Calculus I:
Relevant exercises (Rhyn): Section 4, subsection a), Exercises 3, 4, 5, 6 (without d)), 7, 8, 9, 10, 11, 12 a) and c), 13, 14, 15; Section 6, subsection a), Exercises 1, 2, 3, 4, 5, 6, 7, 8, 10, 15, 18, 20, 23 (without b)); Section 8, Exercises 39, 40, 41, 42 (without d)).
Learning Goals:
To know the definition of a definite integral as the limit of the sum of the areas of rectangles with infinitely small width.
To know and be able to apply the constant rule, sum rule, orientation of integrals and the interval additivity.
To be able to use the geometric interpretation of a definite integral as the area enclosed by the graph of a function and the x-axis. To understand and use the meaning when a definite integral is negative (curve below x-axis).
To be able to compute an indefinite and a definite integral by using the concept of an antiderivative.
To understand the meaning of the integration constant within an indefinite integral.
To understand the geometric and algebraic meaning of a stationary point (local minimum, local maximum, saddle point).
To be able to compute the antiderivative of polynomial, power, exponential and trigonometric functions.
To be able to compute the area enclosed by the graph of two functions and to recognize the geometric situation for the definite integral from an indicated area enclosed by the graph of two functions.
To be able to recognize and use information from differential calculus for solving text exercises based on the geometric configuration of polynomials up to degree 3. To be able to figure out the coefficients of polynomials up to degree 3 from certain geometric situations.
4. Exam: 06.06.2025
4. Exam: 06.06.2025
Vector Geometry I:
Relevant exercises (Rhyn): Section 3, Exercises 1, 2, 3, 4, 5, 6, 7, 9, 10; Section 4, Exercises 1, 2, 3, 4, 5, 6, 7, 8, 16, 17, 18, 19, 20, 21, 22, 24, 25; Section 5, Exercises 1, 2, 5, 7, 8, 9, 12, 13, 14, 15, 16, 17; Section 6, Exercises 1, 2, 3, 4, 6, 7, 8, 10, 11, 12.
Learning Goals:
To know the definition of a vector and its elementary properties and operations: vector addition and scalar multiplication. To know the path principle and being able to geometrically interpret the elementary vector operations.
To understand the properties of the 2- and 3-dimensional coordinate system and interpret vectors within through their definition in components.
To understand and be able to use the concept of a position vector and distinguish between a point and its position vector.
To understand and be able to use the elementary vector operations (vector addition and scalar multiplication) through components.
To be able to compute the length of a vector through its components and use the formula within different situations.
To know about the unit vectors in the 2- and 3-dimensional coordinate system. To know how to produce a vector with length 1 point in the direction of a given vector.
To understand the concept of the scalar product between two vectors and to know both definitions of it (through components and through the angle between the vectors). To be able to use the scalar product in order to get the angle between two vectors. To know the important properties of the scalar product, e.g. the fact that two vectors are normal (perpendicular) if their scalar product vanishes.
To understand the different forms for expressing a straight line in the 2-dimensional coordinate system. To know the expression as the graph of a linear function y=mx+q, the Cartesian and vector form. To be able to compute the slope of a straight line.
To know and be able to use the advantage of the Cartesian and vector form of a line. To be able to read of a normal and direction vector from the Cartesian and vector form respectively. To be able to judge from a given situation which form is more suitable to use.
To know how to produce a vector that stands normal to a given vector in the 2-dimensional coordinate system.
To be able to pass between the different expressions of a straight line. To be able to get the information of whether two straight lines are perpendicular, or parallel by looking at their mathematical expression.
To be able to compute the intersection point and the angle of intersection of two straight lines.
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