MATH 1141 - Calculus I

Course Description

Students study differential calculus for functions of one variable, with applications emphasizing the physical sciences. Topics include calculation and interpretation of limits and derivatives; curve sketching; optimization and related-rate problems; l'Hospital's rule; linear approximation and Newton’s method.

Learning outcomes

• Evaluate a given limit, or determine that the limit does not exist, using appropriate graphical, algebraic or numerical methods. Algebraic methods include simplifying, factoring, rationalizing a numerator or denominator, and using L’Hospital’s Rule.
• Determine the points of discontinuity of a function defined by a graph or formula.
• Use the Intermediate Value Theorem to prove that a given equation has a solution in a given interval.
• State the definition of the derivative, and apply it to find derivatives of simple functions.
• Use differentiation rules to find derivatives of power, exponential, logarithmic, trigonometric and inverse trigonometric functions.
• Apply the Product Rule, Quotient Rule and Chain Rule when appropriate.
• Interpret the derivative of a function as the slope of a tangent line to the graph of the function, and use this idea to obtain derivatives graphically.
• Find derivatives of functions defined implicitly. Use implicit differentiation to differentiate inverse functions. Compute derivatives by logarithmic differentiation. Find the tangent line at a point on a curve defined parametrically.
• Compute the linearization of a function at a given point in its domain. Relate differentials to linear approximation. Use linear approximations and differentials to make estimates. Compute higher order approximations (Taylor polynomials) and use them as estimates.
• Find approximate solutions of equations numerically by Newton’s method.
• State the Mean Value Theorem.
• Find the critical numbers for a function defined by a formula. Find the absolute maximum and minimum values of a function on a closed, bounded interval.
• Use the first derivative of a function to determine the intervals on which it is increasing or decreasing and its local maximum and minimum values. Use the second derivative of a function to determine the intervals on which it is concave up or concave down and to find its inflection points.
• Determine horizontal and vertical asymptotes when they exist. Use all of this information to graph a function without the help of a graphing device.
• Interpret derivatives as rates of change. Use derivatives to compute rates and solve problems involving related rates.
• Solve optimization problems by using derivatives to find extreme values of appropriate objective functions.

Course topics

Unit 1: Limits
Unit 2: Derivatives
Unit 3: Curve Sketching
Unit 4: Applications of Derivatives

Required text and materials

There is no required textbook to purchase. All materials will be provided within the course.

Additional requirements

A good-quality scientific calculator is required.

Assessments

To successfully complete this course, students must achieve a passing grade of 50% or higher on the overall course and 50% or higher on the mandatory Final Exam.

Note: The final exam for this course is only available as a paper exam and must be taken in person at an approved Testing Centre. Please email exams@tru.ca with any questions.

Recommended requisite(s)

Pre-Calculus 12 (minimum grade C+); 
or 
MATH 0610; 
or  
MATH 0630; 
or 
MATH 0633; 
or 
MATH 1000; 
or 
MATH 1001; 

Exclusions

MATH 1130

MATH 1150

MATH 1140

MATH 1157

MATH 1170

MATH 1171