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# Calculus I

Course Code: MATH 1120
Faculty: Science & Technology
Department: Mathematics
Credits: 3.0
Semester: 15 weeks
Learning Format: Lecture, Tutorial
Typically Offered: Fall, Summer, Winter
course overview

MATH 1120 is an introductory calculus course for science students. The course includes limits, continuity, and the differentiation of algebraic, trigonometric, inverse trigonometric, exponential and logarithmic functions. Differentiation techniques are applied to graphing, extrema, related rates, and rectilinear motion, as well as to parametric and polar equations. This course is taught using a graphing calculator.

### Course Content

1. Limits and Continuity
• calculations of limits
• limit theorems
• continuity at a point and on an interval
• essential and removable discontinuities
• Intermediate Value Theorem
2. The Derivative
• rates of change and tangent lines
• differentiation from definition
• differentiation formulas and rules
• chain rule
• implicit differentiation
• higher derivatives
• the differential and differential approximations
• linear approximations
• applications to related rates
3. Inverse Functions: Exponential, Logarithmic and Inverse Trigonometric Functions
• definitions, properties, and graphs
• differentiation of logarithmic and exponential functions (any base)
• logarithmic differentiation
• differentiation of inverse trigonometric functions
• applications to related rates
• limits involving combinations of exponential, logarithmic, trigonometric, and inverse trigonometric functions
• L'Hôpital's rule
4. Graphing and Algebraic Functions
• increasing and decreasing functions
• local extrema
• Rolle's Theorem and Mean Value Theorem
• curve sketching
• concavity; inflection points
• asymptotic behaviour; limits at infinity; infinite limits
• applied maximum and minimum problems
• antidifferentiation
• rectilinear motion
5. Parametric Equations and Polar Coordinates
• parametric representation of curves in
• derivatives and tangent lines of functions in parametric form
• tangent lines to graphs in polar form
• definitions and relationships between polar and Cartesian coordinates
• graphing of r = f(?)
6. Optional Topics (included at the discretion of the instructor).
• a formal limit proof (using epsilonics)
• application of the absolute value and greatest integer functions
• proofs of the rules of differentiation (differentiation formulas) for algebraic functions
• proofs of the differentiation formulas for trigonometric functions from the definition of derivative
• a proof of L'Hôpital's rule for the case of "0/0"
• Newton’s Method

### Methods of Instruction

Lectures, problem sessions and assignments

### Means of Assessment

Evaluation will be carried out in accordance with Douglas College policy. The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester. Evaluation will be based on some of the following criteria:

 Weekly quizzes 0-40% Tests 20-70% Assignments 0-15% Attendance 0-5% Class participation 0-5% Tutorials 0-10% Final examination 30-40%

Note:  All sections of a course with a common final examination will have the same weight given to that examination.

### Learning Outcomes

MATH 1120 is a first course in calculus.  The four-semester sequence of MATH 1120, 1220, 2321, and 2421 provides the foundation for continued studies in science, engineering, computer science, or a major in mathematics.

At the conclusion of this course, the student should be able to:

• find limits involving algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions by inspection as well as by limit laws
• calculate infinite limits and limits at infinity
• apply L'Hôpital's rule to evaluating limits of the types: 0/0, 8/8, 8 - 8, 00,  80, 18
• determine intervals of continuity for a given function
• calculate a derivative from the definition
• differentiate algebraic, trigonometric and inverse trigonometric functions as well as exponential  and logarithmic functions of any base using differentiation formulas and the chain rule
• differentiate functions by logarithmic differentiation
• apply the above differentiation methods to problems involving implicit functions, curve sketching, applied extrema, related rates, and growth and decay problems
• use differentials to estimate the value of a function in the neighbourhood of a given point, and to estimate errors
• apply derivatives to solve problems in velocity and acceleration, related rates, and functional extrema
• interpret and solve optimisation problems
• sketch graphs of functions including rational, trigonometric, logarithmic and exponential functions, identifying intercepts, asymptotes, extrema, intervals of increase and decrease, and concavity
• compute simple antiderivatives, and apply to velocity and acceleration
• recognise and apply the Mean Value Theorem  and  the Intermediate Value Theorem
• be able to convert between parametric and Cartesian forms for simple cases
• use parametric forms to determine first and second derivatives of a function
• sketch graphs of parametric equations and find the slope of a line tangent to the graph at a specified point
• sketch the graph of a polar equation r = f(?), and be able to find intercepts and points of intersection
• find the slope of a line tangent to the graph of a polar equation at a  point (r,?)

course prerequisites

MATH 1110; or Principles of Math 12 with a B or better; or Precalculus 12 with a B or better.

curriculum guidelines

Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester/year of the course, consider the previous version as the applicable version.

course schedule and availability
course transferability

Below shows how this course and its credits transfer within the BC transfer system.

A course is considered university-transferable (UT) if it transfers to at least one of the five research universities in British Columbia: University of British Columbia; University of British Columbia-Okanagan; Simon Fraser University; University of Victoria; and the University of Northern British Columbia.

For more information on transfer visit the BC Transfer Guide and BCCAT websites.

assessments