MATH11110 programs

Calculus 1

This is the first course from a sequence of 3 calculus courses. It deals with limits, continuity, differentiation and integration, applications of the derivative to determine the shape of graphs, evaluation of limits by the L'Hôpital Rule, finding the maximum and the minimum values of functions along with the problems of finding rates. The course ends with the introduction of indefinite and definite integrals, integration by parts, u-substitution, trigonometric substitution, integration of rational functions, improper integrals and applications to area problems.

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ECTS

180

hours in a term

class hours a week

From the Fall 2024 syllabus

What you will learn

•Define the concept of limits and evaluate the limit of a function at a point analytically, graphically and numerically. Limits at infinity. Horizontal asymptotes. Precise definition of limit. L´Hôpital rule.
•Determine whether a function is continuous at a point.
•Know how to formulate word problems in Mathematical language and solve them.
•Use the definition of the derivative to compute derivatives of elementary functions, and compute derivatives using differentiation rules. Distinguish between continuity and differentiability of a function at a point, and justify non-differentiability at a point.
•Find the derivatives of composite functions (chain rule) and implicit functions, and use the techniques of logarithmic differentiation. Hyperbolic functions and its derivatives. Derivatives of the inverse trigonometric functions.

How it is graded

30%

Assignments

One Quiz every week except week 7

30%

Midterm Exam

40%

Final Exam

Workload

180 hours in a term, about 12 a week

In-Class Time 56 hIndependent Study 55 hAssignments 46 hExaminations 18 hGroup Discussions 5 h

Week by week

Books

Calculus, Metric Version

James Stewart & al, 9th

required

Calculus, Volumes 1 and 2

Edwin "Jed" Herman and Gilbert Strang

recommended

Where it fits

NeedsPrecalculus

UnlocksCalculus 2 Calculus 3 Probability and Statistics

Requirements come from syllabi. Check with your advisor.

Rules

Attendance is compulsory. A student missing 25% (32 hours or more) of all instructed hours will be forced to withdraw from the course, per University Academic Regulations.