ADVANCED ENGINEERING MATHEMATICS ENGR. NORMAN C. FRANCISCO DR. MARVIN P. AMOIN REVIEWERS ASEAN ENGR. FRANCISCO B. CULIBRINA, PECE, Ph.D ENGR. VON CYRELL DL. SAN JOSE ENGR. JOHN NEIL B. HERRERA COMPILER ARCH. LYNDON SHERIDAN P. TRINIDAD EDITOR ENGR. MARLON A. BAUTISTA ADVANCED ENGINEERING MATHEMATICS ABOUT THE AUTHORS Jose D. Elveña Jr. Jose D. Elveña is currently a Faculty member of the College of Education of University of Rizal System - Rodriguez Campus. He taught college level Mathematics at Cagayan State UniversityAparri Campus, became an Assistant Professor of the Mathematics and Physical Sciences Department of FEU-Institute of Technology. He also taught at the Mathematics and Mechanics Department of Mapua Institute of Technology. He earned his Bachelor of Secondary Education with Mathematics as his field of specialization. In August 1997, he passed the Licensure Examination for Teachers given by the Professional Regulation Commission. He obtained his Masters degree in Educational Management at Cagayan State University and took Masters of Arts in Teaching major in Mathematics at Eulogio Amang Rodriguez Institute of Technology. Currently, he is pursuing a Doctor of Philosophy major in Mathematics. His professional memberships include the Mathematical Society of the Philippines (MSP) and Mathematics Teachers Association of the Philippines (MTAP). Marlon A. Bautista Engr. Marlon A. Bautista is a Registered Electrical Engineer, graduated from the Technological Institute of the Philippines and with Master of Arts in Teaching Major in Mathematics. He served as the Program Head of the Electrical Engineering Department at the University of Rizal System-Morong from 2003-2015. He served as coach and trainor of various academic competitions such as IIEE National Quiz Show and National Math Wizard, and PCSMT National Math Quiz 2018 with Silver Medal Award. In 2012, he became a Reviewer of Powerhouse Engineering Review Center for Philippine Electrical Code and Technical Subjects. At present He is the Dean of the College of Engineering at the University of Rizal System-Morong in concurrent capacity as the Dean, College of Engineering in Antipolo City Campus. REVIEWERS ENGR. JOHN NEIL B. HERRERA ENGR. MICHAEL B. INTIA JOYCE LYN M. ABAOAG URSM- College of Engineering URS Antipolo City Campus URS Binangonan COMPILER ENGR. MICHAL L. PASCUA URSM- College of Engineering EDITOR JOY SG. CRUZ DISCRETE MATHEMATICS University of Rizal System Bautista, Elveña 2019 ABOUT THE AUTHORS Marlon A. Bautista Engr. Marlon A. Bautista is a Registered Electrical Engineer, graduated from the Technological Institute of the Philippines and with Master of Arts in Teaching Major in Mathematics. He served as the Program Head of the Electrical Engineering Department at the University of Rizal System-Morong from 2003-2015. He served as coach and trainor of various academic competitions such as IIEE National Quiz Show and National Math Wizard, and PCSMT National Math Quiz 2018 with Silver Medal Award. In 2012, he became a Reviewer of Powerhouse Engineering Review Center for Philippine Electrical Code and Technical Subjects. At present He is the Dean of the College of Engineering at the University of Rizal System-Morong in concurrent capacity as the Dean, College of Engineering in Antipolo City Campus. Jose D. Elveña Jr. Jose D. Elveña is currently a Faculty member of the College of Education of University of Rizal System - Rodriguez Campus. He taught college level Mathematics at Cagayan State UniversityAparri Campus, became an Assistant Professor of the Mathematics and Physical Sciences Department of FEU-Institute of Technology. He also taught at the Mathematics and Mechanics Department of Mapua Institute of Technology. He earned his Bachelor of Secondary Education with Mathematics as his field of specialization. In August 1997, he passed the Licensure Examination for Teachers given by the Professional Regulation Commission. He obtained his Masters degree in Educational Management at Cagayan State University and took Masters of Arts in Teaching major in Mathematics at Eulogio Amang Rodriguez Institute of Technology. Currently, he is pursuing a Doctor of Philosophy major in Mathematics. His professional memberships include the Mathematical Society of the Philippines (MSP) and Mathematics Teachers Association of the Philippines (MTAP). REVIEWERS ENGR. NORMAN C. FRANCISCO REE 3rd Placer, September 2012 ENGR. MICHAEL L. PASCUA Electrical Engineer, UPFDU ENGR. VON CYRELL DL. SAN JOSE URSM- College of Engineering URSM- College of Engineering COMPILER URSM- College of Engineering EDITOR DR. MARVIN P. AMOIN University of Rizal System ECE, Ph.D in Mathematical Sciences ENGINEERING DATA ANALYSIS Bautista, Elveña 2019 ABOUT THE AUTHORS Marlon A. Bautista Engr. Marlon A. Bautista is a Registered Electrical Engineer, graduated from the Technological Institute of the Philippines and with Master of Arts in Teaching Major in Mathematics. He served as the Program Head of the Electrical Engineering Department at the University of Rizal System-Morong from 2003-2015. He served as coach and trainor of various academic competitions such as IIEE National Quiz Show and National Math Wizard, and PCSMT National Math Quiz 2018 with Silver Medal Award. In 2012, he became a Reviewer of Powerhouse Engineering Review Center for Philippine Electrical Code and Technical Subjects. At present He is the Dean of the College of Engineering at the University of Rizal System-Morong in concurrent capacity as the Dean, College of Engineering in Antipolo City Campus. Michael L. Pascua Engr. Michael L. Pascua finished his Bachelor of Science in Electrical Engineering at Technological University of the Philippines Manila. He worked as Technical Services Engineer from 2010 to 2016 at MERALCO. From 2016 to present, he is serving as professor of mathematics, engineering sciences and Electrical Engineering subjects at the University of Rizal System. He is also the head of the Electrical Unit for the University Physical Facilities Development Unit of the university. REVIEWERS ENGR. NORMAN C FRANCISCO REE 3rd Placer, September 2012 ENGR. JOHN NEIL B. HERRERA Electrical Engineer JOSE D. ELVEÑA, JR. MS Mathematics URSM- College of Engineering URSM- College of Engineering URS-Rodriguez COMPILER ARCH. LYNDON SHERIDAN P. TRINIDAD, UPFDU Head, URS EDITOR DR. MARVIN P. AMOIN University of Rizal System ECE, Ph.D in Mathematical Sciences ELECTRICAL CIRCUITS 1 Bautista, Pascua 2019 ABOUT THE AUTHORS Marlon A. Bautista Engr. Marlon A. Bautista is a Registered Electrical Engineer, graduated from the Technological Institute of the Philippines and with Master of Arts in Teaching Major in Mathematics. He served as the Program Head of the Electrical Engineering Department at the University of Rizal System-Morong from 2003-2015. He served as coach and trainor of various academic competitions such as IIEE National Quiz Show and National Math Wizard, and PCSMT National Math Quiz 2018 with Silver Medal Award. In 2012, he became a Reviewer of Powerhouse Engineering Review Center for Philippine Electrical Code and Technical Subjects. At present He is the Dean of the College of Engineering at the University of Rizal System-Morong in concurrent capacity as the Dean, College of Engineering in Antipolo City Campus. Jose D. Elveña Jr. Jose D. Elveña is currently a Faculty member of the College of Education of University of Rizal System - Rodriguez Campus. He taught college level Mathematics at Cagayan State UniversityAparri Campus, became an Assistant Professor of the Mathematics and Physical Sciences Department of FEU-Institute of Technology. He also taught at the Mathematics and Mechanics Department of Mapua Institute of Technology. He earned his Bachelor of Secondary Education with Mathematics as his field of specialization. In August 1997, he passed the Licensure Examination for Teachers given by the Professional Regulation Commission. He obtained his Masters degree in Educational Management at Cagayan State University and took Masters of Arts in Teaching major in Mathematics at Eulogio Amang Rodriguez Institute of Technology. Currently, he is pursuing a Doctor of Philosophy major in Mathematics. His professional memberships include the Mathematical Society of the Philippines (MSP) and Mathematics Teachers Association of the Philippines (MTAP). REVIEWERS ENGR. JOHN NEIL B. HERRERA Electrical Engineer ENGR. MICHAEL B. INTA MsED-Mathematics EMMANUEL M. LLARENAS URSM- College of Engineering URSM- Antipolo City Campus COMPILER URS-Rodriguez EDITOR DR. MARVIN P. AMOIN University of Rizal System ECE, Ph.D in Mathematical Sciences ELEMENTARY STATISTICS Bautista, Elveña 2019 ABOUT THE AUTHORS Jose D. Elveña Jr. Jose D. Elveña is currently a Faculty member of the College of Education of University of Rizal System - Rodriguez Campus. He taught college level Mathematics at Cagayan State UniversityAparri Campus, became an Assistant Professor of the Mathematics and Physical Sciences Department of FEU-Institute of Technology. He also taught at the Mathematics and Mechanics Department of Mapua Institute of Technology. He earned his Bachelor of Secondary Education with Mathematics as his field of specialization. In August 1997, he passed the Licensure Examination for Teachers given by the Professional Regulation Commission. He obtained his Masters degree in Educational Management at Cagayan State University and took Masters of Arts in Teaching major in Mathematics at Eulogio Amang Rodriguez Institute of Technology. Currently, he is pursuing a Doctor of Philosophy major in Mathematics. His professional memberships include the Mathematical Society of the Philippines (MSP) and Mathematics Teachers Association of the Philippines (MTAP). Marlon A. Bautista Engr. Marlon A. Bautista is a Registered Electrical Engineer, graduated from the Technological Institute of the Philippines and with Master of Arts in Teaching Major in Mathematics. He served as the Program Head of the Electrical Engineering Department at the University of Rizal System-Morong from 2003-2015. He served as coach and trainor of various academic competitions such as IIEE National Quiz Show and National Math Wizard, and PCSMT National Math Quiz 2018 with Silver Medal Award. In 2012, he became a Reviewer of Powerhouse Engineering Review Center for Philippine Electrical Code and Technical Subjects. At present He is the Dean of the College of Engineering at the University of Rizal System-Morong in concurrent capacity as the Dean, College of Engineering in Antipolo City Campus. REVIEWERS ENGR. NORMAN C FRANCISCO REE 3rd Placer, September 2012 ENGR. MICHAEL L. PASCUA Electrical Engineer, UPFDU URSM- College of Engineering URSM- College of Engineering COMPILER ENGR. JOHN NEIL B. HERRERA-URSM EDITOR DR. MARVIN P. AMOIN University of Rizal System ECE, Ph.D in Mathematical Sciences INTEGRAL CALCULUS Bautista, Elveña 2019 ABOUT THE AUTHORS Jose D. Elveña Jr. Jose D. Elveña is currently a Faculty member of the College of Education of University of Rizal System - Rodriguez Campus. He taught college level Mathematics at Cagayan State UniversityAparri Campus, became an Assistant Professor of the Mathematics and Physical Sciences Department of FEU-Institute of Technology. He also taught at the Mathematics and Mechanics Department of Mapua Institute of Technology. He earned his Bachelor of Secondary Education with Mathematics as his field of specialization. In August 1997, he passed the Licensure Examination for Teachers given by the Professional Regulation Commission. He obtained his Masters degree in Educational Management at Cagayan State University and took Masters of Arts in Teaching major in Mathematics at Eulogio Amang Rodriguez Institute of Technology. Currently, he is pursuing a Doctor of Philosophy major in Mathematics. His professional memberships include the Mathematical Society of the Philippines (MSP) and Mathematics Teachers Association of the Philippines (MTAP). Marlon A. Bautista Engr. Marlon A. Bautista is a Registered Electrical Engineer, graduated from the Technological Institute of the Philippines and with Master of Arts in Teaching Major in Mathematics. He served as the Program Head of the Electrical Engineering Department at the University of Rizal System-Morong from 2003-2015. He served as coach and trainor of various academic competitions such as IIEE National Quiz Show and National Math Wizard, and PCSMT National Math Quiz 2018 with Silver Medal Award. In 2012, he became a Reviewer of Powerhouse Engineering Review Center for Philippine Electrical Code and Technical Subjects. At present He is the Dean of the College of Engineering at the University of Rizal System-Morong in concurrent capacity as the Dean, College of Engineering in Antipolo City Campus. REVIEWER ENGR. MARLON A. BAUTISTA MAT-Mathematics ENGR. MICHAEL B. INTIA URSM-College of Engineering COMPILER URS-Antipolo City MAED-Mathematics EDITOR EMMANUEL LLARENAS MAT-Mathematics MATHEMATICAL LOGIC URS-Rodriguez Campus Bautista, Elveña 2019
