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Catalog Description Prerequisite: Completion of MATH 12 and MATH 27, or MATH 29 with grades of "C" or better, or appropriate placement Hours: 72 lecture Description: Introduction to differential and integral calculus. Content includes limits, continuity, differentiation and integration of algebraic, trigonometric, exponential, logarithmic, hyperbolic and other transcendental functions; as well as application problems. (C-ID MATH 210) (combined with MATH 31, C-ID MATH 900S) (CSU, UC-with unit limitation) Course Student Learning Outcomes CSLO #1: Evaluate limits of functions using limit laws, the definition of a limit, or L'Hospital's Rule; and utilize limits to determine continuity. CSLO #2: Calculate derivatives and integrals of algebraic and transcendental functions. CSLO #3: Translate, model, and solve applied problems utilizing derivatives and integrals. CSLO #4: Construct graphs of algebraic and transcendental functions using their derivatives. CSLO #5: Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems. Effective Term Fall 2025 Course Type Credit - Degree-applicable Contact Hours 72 Outside of Class Hours 144 Total Student Learning Hours 216 Course Objectives 1. Compute the limit of a function. 2. Find the derivative of a function using the limit definition of a derivative. 3. Find the equation of a tangent line to a function. 4. Compute derivatives using differentiation formulas. 5. Use differentiation to solve applications such as related rate problems and optimization problems. 6. Apply implicit differentiation. 7. Graph functions using first derivatives, second derivatives, and limits. 8. Evaluate a definite integral as the limit of a Riemann Sum. 9. Evaluate integrals using the Fundamental Theorem of Calculus. 10. Apply integration to find area. General Education Information Approved College Associate Degree GE Applicability AA/AS - Comm & Analyt Thinking AA/AS - Mathematical Skills AA/AS - Physical Sciences CSU GE Applicability (Recommended-requires CSU approval) CSUGE - B4 Math/Quantitative Reasoning Cal-GETC Applicability (Recommended - Requires External Approval) Cal-GETC 2 - Mathematical Concepts IGETC Applicability (Recommended-requires CSU/UC approval) IGETC - 2A Math/Quan Reasoning Articulation Information CSU Transferable UC Transferable Methods of Evaluation Problem Solving Examinations Example: 1. A particle moves on a vertical line so that its coordinate at time t is y = t^3 - 12t + 3, for t > 0. Find the velocity and acceleration functions. When is the particle moving upwards and when is it moving downwards? Find the distance the particle moves in the time interval t = 1 to t = 3. This problem is graded for correct method and accuracy. 2. Find an equation of the line through the point (3, 5) that cuts off the least area from the first quadrant. This problem is graded for correct method and accuracy. Repeatable No Methods of Instruction Lecture/Discussion Distance Learning Lecture: Interactive lecture format to develop the concept of what a derivative represents, given a variety of functions (e.g., rational, polynomial, trigonometric, exponential, logarithmic). To help students see the commonalities and differences between the derivatives of each type of function, the instructor will incorporate algebraic analysis through equations and visual analysis through graphing. Students will participate verbally and will work several examples. (Objectives 2 & 4) In class, small group collaborative learning activities will focus on applied physics problems involving derivatives. These will include analysis of velocity, acceleration, and other instantaneous rates of change. After an instructor lecture on derivatives, students will practice reading problems, interpreting problems, and developing solutions with peers. (Objective 7) Distance Learning Video lectures develop the concept of what a derivative represents, given a variety of functions (e.g., rational, polynomial, trigonometric, exponential, logarithmic). To help students see the commonalities and differences between the derivatives of each type of function, the instructor will incorporate algebraic analysis through equations and visual analysis through graphing. Students will participate in a discussion board to post work from several examples for peer review. (Objectives 2 & 4) In small virtual groups students will be create a wiki-page showing an applied physics problems involving derivatives. These will include analysis of velocity, acceleration, and other instantaneous rates of change. After a video lecture on derivatives, students will practice reading problems, interpreting problems, and developing solutions to post for peer review. (Objective 7) Typical Out of Class Assignments Reading Assignments 1. Read in your textbook how the first and second derivative of a function influence the graph of the function and be prepared to discuss in class. 2. Research online the history of the development of calculus, including Newton and Leibniz and be prepared to discuss in class. Writing, Problem Solving or Performance 1. Write a report on the historical and mathematical origins of l'Hospital's rule. 2. After reading about Newton's and Leibniz's development of calculus, write a 3 - 5 paragraph essay comparing and contrasting each approach. Other (Term projects, research papers, portfolios, etc.) Required Materials Calculus: Early Transcendentals Author: Gillett, Schulz Publisher: Pearson Publication Date: 2019 Text Edition: 3rd Classic Textbook?: No OER Link: OER: Calculus: Early Transcendentals Author: James Stewart Publisher: Cengage Learning Publication Date: 2016 Text Edition: 8th Classic Textbook?: No OER Link: OER: Other materials and-or supplies required of students that contribute to the cost of the course.

Catalog Description Prerequisite: Completion of Math 0030 with grade of "C" or better Advisory: Completion of Math 0031 with grade of "C" or better strongly recommended Hours: 54 lecture Description: Develops the techniques and theory needed to solve and classify systems of linear equations. Solution techniques include row operations, Gaussian elimination, and matrix algebra. Investigates the properties of vectors in two and three dimensions, leading to the notion of an abstract vector space. Vector space and matrix theory are presented including topics such as inner products, norms, orthogonality, eigenvalues, eigenspaces, and linear transformations. Selected applications of linear algebra are included. (CSU) Course Student Learning Outcomes CSLO #1: Utilize theorems from linear algebra and use matrices to solve systems of equations,and to classify sets and mappings. CSLO #2: Present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems. CSLO #3: Prove basic results in linear algebra using appropriate proof-writing techniques. Effective Term Fall 2026 Course Type Credit - Degree-applicable Contact Hours 54 Outside of Class Hours 108 Total Student Learning Hours 162 Course Objectives Upon successful completion of the course, students will be able to: Find solutions of systems of equations using various methods appropriate to lower division linear algebra; Use bases and orthonormal bases to solve problems in linear algebra; Find the dimension of spaces such as those associated with matrices and linear transformations; Find eigenvalues and eigenvectors and use them in applications; and Prove basic results in linear algebra using appropriate proof-writing techniques such as linear independence of vectors; properties of subspaces; linearity, injectivity and surjectivity of functions; and properties of eigenvectors and eigenvalues. General Education Information Approved College Associate Degree GE Applicability AA/AS - Mathematical Concepts and Quantitative Reasoning CSU GE Applicability (Recommended-requires CSU approval) Cal-GETC Applicability (Recommended - Requires External Approval) Cal-GETC 2 - Mathematical Concepts IGETC Applicability (Recommended-requires CSU/UC approval) Articulation Information CSU Transferable UC Transferable Methods of Evaluation Problem Solving Examinations Example: Prove that P3 is a vector space by verifying that the set P3 satisfies each of the axioms for a vector space. This problem is graded for completeness and accuracy. Students need to verify each of the ten vector space axioms. Reports Example: In a report, give specific examples of 5 different types of lattices and prove the corresponding bases for each of your examples. In a summary, compare your proofs performed with lattices with the proofs for bases you performed with vector spaces and explain how they are similar and different. This report is graded on completeness, and accuracy of the proofs. The student will also be graded on their summary and their analytical comparison of the proofs in the two mathematical structures. Repeatable No Methods of Instruction Lecture/Discussion Lecture: The students and instructor will engage in an interactive discussion concerning whether P3 with certain restrictions constitutes a vector space. The discussion will lead to a conclusion that prompts the instructor to introduce the writing technique necessary for students to verify that such a set is a vector space or introduce the writing technique necessary for students to verify such a set is not a vector space. Students will then get an opportunity to practice such writing techniques on other sets provided by the instructor. Typical Out of Class Assignments Reading Assignments Read from the text and research a mathematical structure similar to a vector space called a lattice. Be prepared to discuss your findings in class. Writing, Problem Solving or Performance Consider the linear transformation T: R3 to R defined by the inner product of v with a fixed nonzero vector u, also in R3. Find Ker(T) and interpret this geometrically. Find Rng(T), and the dimensions of both Ker(T) and Rng(T). Other (Term projects, research papers, portfolios, etc.) Required Materials Linear Algebra Author: Waldron, Cherney, and Denton Publisher: Libre Texts Publication Date: 2025 Text Edition: Classic Textbook?: No OER Link: OER: https://math.libretexts.org/Bookshelves/Linear_Algebra/Map%3A_Linear_Algebra_(Waldron_Cherney_and_Denton) Introduction to Linear Algebra Author: Gilbert Strang Publisher: Wellesey-Cambridge Press Publication Date: 2023 Text Edition: 6th Classic Textbook?: No OER Link: OER: Other materials and-or supplies required of students that contribute to the cost of the course.